Solving Equations - Algebra II (2024)

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Algebra II Help » Basic Single-Variable Algebra » Equations » Solving Equations

Example Question #1 : Linear Systems With Three Variables

Solve this system of equations.

Solving Equations - Algebra II (1)

Solving Equations - Algebra II (2)

Solving Equations - Algebra II (3)

Possible Answers:

Solving Equations - Algebra II (4), Solving Equations - Algebra II (5), Solving Equations - Algebra II (6)

Solving Equations - Algebra II (7), Solving Equations - Algebra II (8), Solving Equations - Algebra II (9)

Solving Equations - Algebra II (10), Solving Equations - Algebra II (11), Solving Equations - Algebra II (12)

Solving Equations - Algebra II (13), Solving Equations - Algebra II (14), Solving Equations - Algebra II (15)

Solving Equations - Algebra II (16), Solving Equations - Algebra II (17), Solving Equations - Algebra II (18)

Correct answer:

Solving Equations - Algebra II (19), Solving Equations - Algebra II (20), Solving Equations - Algebra II (21)

Explanation:

Equation 1: Solving Equations - Algebra II (22)

Equation 2: Solving Equations - Algebra II (23)

Equation 3: Solving Equations - Algebra II (24)

Adding the terms of the first and second equations together will yield Solving Equations - Algebra II (25).

Then, add that to the third equation so that the y and z terms are eliminated. You will get Solving Equations - Algebra II (26).

This tells us that x = 1. Plug this x = 1 back into the systems of equations.

Solving Equations - Algebra II (27)

Solving Equations - Algebra II (28)

Solving Equations - Algebra II (29)

Now, we can do the rest of the problem by using the substitution method. We'll take the third equation and use it to solve for y.

Solving Equations - Algebra II (30)

Solving Equations - Algebra II (31)

Solving Equations - Algebra II (32)

Plug this y-equation into the first equation (or second equation; it doesn't matter) to solve for z.

Solving Equations - Algebra II (33)

Solving Equations - Algebra II (34)

Solving Equations - Algebra II (35)

Solving Equations - Algebra II (36)

Solving Equations - Algebra II (37)

We can use this z value to find y

Solving Equations - Algebra II (38)

Solving Equations - Algebra II (39)

Solving Equations - Algebra II (40)

So the solution set is x = 1, y = 2, and z = –5/3.

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Example Question #2 : Solving Equations

Solve for Solving Equations - Algebra II (41):Solving Equations - Algebra II (42)

Possible Answers:

Solving Equations - Algebra II (43)

Solving Equations - Algebra II (44)

Solving Equations - Algebra II (45)

Solving Equations - Algebra II (46)

Correct answer:

Solving Equations - Algebra II (47)

Explanation:

To solve this problem we can first addSolving Equations - Algebra II (48)to each side of the equation yieldingSolving Equations - Algebra II (49)

Then we take the square root of both sides to getSolving Equations - Algebra II (50)

Then we calculate the square root ofSolving Equations - Algebra II (51)which isSolving Equations - Algebra II (52).

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Example Question #3 : Solving Equations

Solve this system of equations forSolving Equations - Algebra II (53):

Solving Equations - Algebra II (54)

Solving Equations - Algebra II (55)

Correct answer:

Solving Equations - Algebra II (61)

Explanation:

Multiply the top equation by 3 on both sides, then add the second equation to eliminate theSolving Equations - Algebra II (62)terms:

Solving Equations - Algebra II (63)

Solving Equations - Algebra II (64)

Solving Equations - Algebra II (65)

Solving Equations - Algebra II (66)

Solving Equations - Algebra II (67)

Solving Equations - Algebra II (68)

Solving Equations - Algebra II (69)

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Example Question #91 : Factoring Polynomials

Solve forSolving Equations - Algebra II (70).

Solving Equations - Algebra II (71)

Possible Answers:

Solving Equations - Algebra II (72)

Solving Equations - Algebra II (73)

Solving Equations - Algebra II (74)

Solving Equations - Algebra II (75)

Solving Equations - Algebra II (76)

Correct answer:

Solving Equations - Algebra II (77)

Explanation:

Solving Equations - Algebra II (78)

Multiply both sides by 3:

Solving Equations - Algebra II (79)

Solving Equations - Algebra II (80)

Distribute:

Solving Equations - Algebra II (81)

Subtract Solving Equations - Algebra II (82)from both sides:

Solving Equations - Algebra II (83)

Add the Solving Equations - Algebra II (84)terms together, and subtract Solving Equations - Algebra II (85)from both sides:

Solving Equations - Algebra II (86)

Divide both sides bySolving Equations - Algebra II (87):

Solving Equations - Algebra II (88)

Simplify:

Solving Equations - Algebra II (89)

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Example Question #21 : Equations / Solution Sets

Solve for Solving Equations - Algebra II (90):

Solving Equations - Algebra II (91)

Possible Answers:

Solving Equations - Algebra II (92)

Solving Equations - Algebra II (93)

Solving Equations - Algebra II (94)

Solving Equations - Algebra II (95)

Solving Equations - Algebra II (96)

Correct answer:

Solving Equations - Algebra II (97)

Explanation:

Distribute the x through the parentheses:

x2 –2x = x2 – 8

Subtract x2 from both sides:

–2x = –8

Divide both sides by –2:

x = 4

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Example Question #1 : Solving Equations

Solve for Solving Equations - Algebra II (98):.

Solving Equations - Algebra II (99)

Possible Answers:

Solving Equations - Algebra II (100)

Solving Equations - Algebra II (101)

Solving Equations - Algebra II (102)

Solving Equations - Algebra II (103)

Solving Equations - Algebra II (104)

Correct answer:

Solving Equations - Algebra II (105)

Explanation:

First factor the expression by pulling out Solving Equations - Algebra II (106):

Solving Equations - Algebra II (107)

Solving Equations - Algebra II (108)

Factor the expression in parentheses by recognizing that it is a difference of squares:

Solving Equations - Algebra II (109)

Set each term equal to 0 and solve for the x values:

Solving Equations - Algebra II (110)

Solving Equations - Algebra II (111)

Solving Equations - Algebra II (112)

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Example Question #1 : Systems Of Equations

Solve the system of equations.

Solving Equations - Algebra II (113)

Solving Equations - Algebra II (114)

Possible Answers:

Solving Equations - Algebra II (115)

Solving Equations - Algebra II (116)

Solving Equations - Algebra II (117)

Solving Equations - Algebra II (118)

None of the other answers are correct.

Correct answer:

Solving Equations - Algebra II (119)

Explanation:

IsolateSolving Equations - Algebra II (120) in the first equation.

Solving Equations - Algebra II (121)

Plug Solving Equations - Algebra II (122) into the second equation to solve for Solving Equations - Algebra II (123).

Solving Equations - Algebra II (124)

Solving Equations - Algebra II (125)

Solving Equations - Algebra II (126)

Solving Equations - Algebra II (127)

Solving Equations - Algebra II (128)

Plug Solving Equations - Algebra II (129) into the first equation to solve for Solving Equations - Algebra II (130).

Solving Equations - Algebra II (131)

Solving Equations - Algebra II (132)

Solving Equations - Algebra II (133)

Now we have both the Solving Equations - Algebra II (134) and Solving Equations - Algebra II (135) values and can express them as a point: Solving Equations - Algebra II (136).

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Example Question #1 : Solving Equations

Solve forSolving Equations - Algebra II (137) and Solving Equations - Algebra II (138).

Solving Equations - Algebra II (139)

Solving Equations - Algebra II (140)

Possible Answers:

Solving Equations - Algebra II (141)

Solving Equations - Algebra II (142)

Solving Equations - Algebra II (143)

Cannot be determined.

Solving Equations - Algebra II (144)

Correct answer:

Solving Equations - Algebra II (145)

Explanation:

1st equation: Solving Equations - Algebra II (146)

2nd equation: Solving Equations - Algebra II (147)

Subtract the 2nd equation from the 1st equation to eliminate the "2y" from both equations and get an answer for x:

Solving Equations - Algebra II (148)

Plug the value ofSolving Equations - Algebra II (149) into either equation and solve for Solving Equations - Algebra II (150):

Solving Equations - Algebra II (151)

Solving Equations - Algebra II (152)

Solving Equations - Algebra II (153)

Solving Equations - Algebra II (154)

Solving Equations - Algebra II (155)

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Example Question #9 : Solving Equations

What is a solution to this system of equations:

Solving Equations - Algebra II (156)

Possible Answers:

Solving Equations - Algebra II (157)

Solving Equations - Algebra II (158)

Solving Equations - Algebra II (159)

Solving Equations - Algebra II (160)

Solving Equations - Algebra II (161)

Correct answer:

Solving Equations - Algebra II (162)

Explanation:

Step 1:Multiply first equation by2and add the result to the second equation. The result is:

Solving Equations - Algebra II (163)

Step 2:Multiply first equation by3and add the result to the third equation. The result is:

Solving Equations - Algebra II (164)

Step 3:Multiply second equation by23and add the result to the third equation. The result is:

Solving Equations - Algebra II (165)

Step 4:solve forz.

Solving Equations - Algebra II (166)

Solving Equations - Algebra II (167)

Step 5:solve fory.

Solving Equations - Algebra II (168)

Solving Equations - Algebra II (169)

Solving Equations - Algebra II (170)

Step 6:solve forxby substitutingy=2andz=1into the first equation.

Solving Equations - Algebra II (171)

Solving Equations - Algebra II (172)

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Example Question #10 : Solving Equations

What is a solution to this system of equations?

Solving Equations - Algebra II (173)

Possible Answers:

Solving Equations - Algebra II (174)

Solving Equations - Algebra II (175)

Solving Equations - Algebra II (176)

Solving Equations - Algebra II (177)

Solving Equations - Algebra II (178)

Correct answer:

Solving Equations - Algebra II (179)

Explanation:

  1. Solving Equations - Algebra II (180)
  2. Solving Equations - Algebra II (181)

Substitute equation 2. into equation 1.,

Solving Equations - Algebra II (182)

Solving Equations - Algebra II (183)

Solving Equations - Algebra II (184)

so,Solving Equations - Algebra II (185)

Substitute Solving Equations - Algebra II (186)into equation2:

Solving Equations - Algebra II (187)

so, the solution isSolving Equations - Algebra II (188).

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Solving Equations - Algebra II (2024)

FAQs

How to pass algebra 2 easily? ›

Consider forming a study group. Working with your fellow students to solve problems and going over algebraic concepts is a great way to succeed in an Algebra 2 class. You can also find out if your school offers a math study lab or tutors. Taking advantage of these resources can make passing Algebra 2 a lot easier.

Why is algebra 2 so hard for me? ›

Because Algebra 2 builds on and combines material from past math classes as well as includes additional miscellaneous concepts, it is inherently a level above Algebra 1 in terms of difficulty; however, if the student did not struggle with Algebra 1, the addition of new material introduced in Algebra 2 should not be too ...

How do you know if your algebra answer is correct? ›

After you solve the equation, you can check if the answer is correct by inserting the solution into both sides. You then check if the value of the expression on the left hand side (LHS) is equal to the value of the expression on the right hand side (RHS).

How to check your answer when solving a system of equations? ›

If you are asked if a point is a solution to an equation, we replace the variables with the given values and see if the 2 sides of the equation are equal (so is a solution), or not equal (so not a solution). A solution to a system of equations means the point must work in both equations in the system.

Is algebra 2 harder than calculus? ›

Which is generally considered more challenging, algebra or calculus? The perception of difficulty varies among individuals, but calculus is often considered more challenging due to its introduction of new concepts like limits, derivatives, and integrals, building upon the foundation laid by algebra.

Is it okay to skip algebra 2? ›

In general, skipping Algebra II is a bad idea if you plan on going to a college or university since they have the choice to reject you, There could also be other hidden consequences for not completing Algebra successfully.

Do most people fail algebra? ›

Algebra I is the single most failed course in American high schools. Thirty-three percent of students in California, for example, took Algebra I at least twice during their high school careers.

Is algebra 2 or Geometry harder? ›

Geometry is simpler than algebra 2. So if you want to look at these three courses in order of difficulty, it would be algebra 1, geometry, then algebra 2. Geometry does not use any math more complicated than the concepts learned in algebra 1.

Is algebra 2 or pre-calc harder? ›

As for difficulty, pre-calc is generally considered a bit more challenging than Algebra 2 because it combines several mathematical concepts from previous courses and introduces new topics.

What happens if you fail algebra? ›

Students who fail Algebra I are required to recover the credit during high school to earn a diploma, and online credit recovery courses have become a popular strategy in schools and districts around the country.

What is the easiest way to solve system of equations? ›

The Matrix method is the easiest way to solve a set of linear equations, because it is straightforward and a step-by-step method, and it boils down to the same thing as the elimination method that most people are familiar with.

What is the correct way to check the solved equation? ›

We check a solution to an equation by replacing the variable in the equation with the value of the solution. A solution should result in a true statement when simplified.

How can I solve algebra faster? ›

What are some tips and tricks to solve algebra problems faster and more accurately?
  1. Review the basics. Be the first to add your personal experience.
  2. Simplify the problem.
  3. Use substitution and elimination. ...
  4. Check your answers. ...
  5. Practice and learn from mistakes. ...
  6. Apply algebra to real-life situations. ...
  7. Here's what else to consider.
Mar 21, 2023

What happens if you fail Algebra 2? ›

In general, you will need to make up the failed class in order to graduate. You can do this by taking the class again during the summer or next school year, or by completing a credit recovery program.

Is algebra 2 harder than geometry? ›

Geometry is simpler than algebra 2. So if you want to look at these three courses in order of difficulty, it would be algebra 1, geometry, then algebra 2. Geometry does not use any math more complicated than the concepts learned in algebra 1.

Is algebra 2 harder than pre-calc? ›

As for difficulty, pre-calc is generally considered a bit more challenging than Algebra 2 because it combines several mathematical concepts from previous courses and introduces new topics.

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