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Systems of Equations

Description: This quiz is designed to assess your understanding of solving systems of equations using various methods, including substitution, elimination, and graphing.
Number of Questions: 14
Created by:
Tags: systems of equations substitution elimination graphing
Attempted 0/14 Correct 0 Score 0

Solve the following system of equations using the substitution method: 2x + 3y = 11 x - y = 1

  1. (x, y) = (2, 3)

  2. (x, y) = (3, 2)

  3. (x, y) = (4, 1)

  4. (x, y) = (1, 4)


Correct Option: A
Explanation:

To solve using substitution, solve one equation for one variable and substitute it into the other equation. Solving x - y = 1 for x, we get x = y + 1. Substituting this into 2x + 3y = 11, we get 2(y + 1) + 3y = 11. Solving for y, we get y = 2. Substituting y = 2 back into x = y + 1, we get x = 3. Therefore, the solution is (x, y) = (2, 3).

Solve the following system of equations using the elimination method: 3x + 2y = 7 2x - 3y = 1

  1. (x, y) = (2, 1)

  2. (x, y) = (1, 2)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)


Correct Option: A
Explanation:

To solve using elimination, multiply one or both equations by a constant to make the coefficients of one variable the same. Multiplying the first equation by 2 and the second equation by 3, we get: 6x + 4y = 14 6x - 9y = 3 Subtracting the second equation from the first, we get: 13y = 11 Solving for y, we get y = 1. Substituting y = 1 back into either of the original equations, we can solve for x. Using the first equation, we get 3x + 2(1) = 7, which gives x = 2. Therefore, the solution is (x, y) = (2, 1).

Solve the following system of equations using the graphing method: y = 2x + 1 y = x - 3

  1. (x, y) = (-2, -5)

  2. (x, y) = (1, -2)

  3. (x, y) = (2, -1)

  4. (x, y) = (3, 1)


Correct Option: C
Explanation:

To solve using graphing, graph both equations on the same coordinate plane and find the point of intersection. Graphing the equations, we can see that they intersect at the point (2, -1). Therefore, the solution is (x, y) = (2, -1).

Solve the following system of equations: x + 2y = 5 3x - y = 1

  1. (x, y) = (1, 2)

  2. (x, y) = (2, 1)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)


Correct Option: A
Explanation:

To solve this system of equations, we can use the substitution method. Solving the first equation for x, we get x = 5 - 2y. Substituting this into the second equation, we get 3(5 - 2y) - y = 1. Solving for y, we get y = 2. Substituting y = 2 back into x = 5 - 2y, we get x = 1. Therefore, the solution is (x, y) = (1, 2).

Solve the following system of equations: 2x + 3y = 7 4x - 2y = 10

  1. (x, y) = (2, 1)

  2. (x, y) = (1, 2)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)


Correct Option: A
Explanation:

To solve this system of equations, we can use the elimination method. Multiplying the first equation by 2 and the second equation by 3, we get: 4x + 6y = 14 12x - 6y = 30 Adding the two equations, we get: 16x = 44 Solving for x, we get x = 2. Substituting x = 2 back into either of the original equations, we can solve for y. Using the first equation, we get 2(2) + 3y = 7, which gives y = 1. Therefore, the solution is (x, y) = (2, 1).

Solve the following system of equations: y = x^2 - 1 y = 2x - 3

  1. (x, y) = (2, 1)

  2. (x, y) = (1, 2)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)


Correct Option: A
Explanation:

To solve this system of equations, we can substitute the first equation into the second equation. Substituting y = x^2 - 1 into y = 2x - 3, we get x^2 - 1 = 2x - 3. Rearranging the equation, we get x^2 - 2x + 2 = 0. Factoring the quadratic equation, we get (x - 2)(x - 1) = 0. Setting each factor equal to zero, we get x = 2 and x = 1. Substituting x = 2 back into the first equation, we get y = 2^2 - 1 = 3. Therefore, the solution is (x, y) = (2, 1).

Solve the following system of equations: 3x + 2y = 5 2x - y = 1

  1. (x, y) = (1, 2)

  2. (x, y) = (2, 1)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)


Correct Option: A
Explanation:

To solve this system of equations, we can use the substitution method. Solving the second equation for y, we get y = 2x - 1. Substituting this into the first equation, we get 3x + 2(2x - 1) = 5. Solving for x, we get x = 1. Substituting x = 1 back into the second equation, we get y = 2(1) - 1 = 1. Therefore, the solution is (x, y) = (1, 2).

Solve the following system of equations: 2x + 3y = 7 4x - 2y = 10

  1. (x, y) = (2, 1)

  2. (x, y) = (1, 2)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)


Correct Option: A
Explanation:

To solve this system of equations, we can use the elimination method. Multiplying the first equation by 2 and the second equation by 3, we get: 4x + 6y = 14 12x - 6y = 30 Adding the two equations, we get: 16x = 44 Solving for x, we get x = 2. Substituting x = 2 back into either of the original equations, we can solve for y. Using the first equation, we get 2(2) + 3y = 7, which gives y = 1. Therefore, the solution is (x, y) = (2, 1).

Solve the following system of equations: y = x^2 - 1 y = 2x - 3

  1. (x, y) = (2, 1)

  2. (x, y) = (1, 2)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)


Correct Option: A
Explanation:

To solve this system of equations, we can substitute the first equation into the second equation. Substituting y = x^2 - 1 into y = 2x - 3, we get x^2 - 1 = 2x - 3. Rearranging the equation, we get x^2 - 2x + 2 = 0. Factoring the quadratic equation, we get (x - 2)(x - 1) = 0. Setting each factor equal to zero, we get x = 2 and x = 1. Substituting x = 2 back into the first equation, we get y = 2^2 - 1 = 3. Therefore, the solution is (x, y) = (2, 1).

Solve the following system of equations: 3x + 2y = 5 2x - y = 1

  1. (x, y) = (1, 2)

  2. (x, y) = (2, 1)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)


Correct Option: A
Explanation:

To solve this system of equations, we can use the substitution method. Solving the second equation for y, we get y = 2x - 1. Substituting this into the first equation, we get 3x + 2(2x - 1) = 5. Solving for x, we get x = 1. Substituting x = 1 back into the second equation, we get y = 2(1) - 1 = 1. Therefore, the solution is (x, y) = (1, 2).

Solve the following system of equations: 2x + 3y = 7 4x - 2y = 10

  1. (x, y) = (2, 1)

  2. (x, y) = (1, 2)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)


Correct Option: A
Explanation:

To solve this system of equations, we can use the elimination method. Multiplying the first equation by 2 and the second equation by 3, we get: 4x + 6y = 14 12x - 6y = 30 Adding the two equations, we get: 16x = 44 Solving for x, we get x = 2. Substituting x = 2 back into either of the original equations, we can solve for y. Using the first equation, we get 2(2) + 3y = 7, which gives y = 1. Therefore, the solution is (x, y) = (2, 1).

Solve the following system of equations: y = x^2 - 1 y = 2x - 3

  1. (x, y) = (2, 1)

  2. (x, y) = (1, 2)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)


Correct Option: A
Explanation:

To solve this system of equations, we can substitute the first equation into the second equation. Substituting y = x^2 - 1 into y = 2x - 3, we get x^2 - 1 = 2x - 3. Rearranging the equation, we get x^2 - 2x + 2 = 0. Factoring the quadratic equation, we get (x - 2)(x - 1) = 0. Setting each factor equal to zero, we get x = 2 and x = 1. Substituting x = 2 back into the first equation, we get y = 2^2 - 1 = 3. Therefore, the solution is (x, y) = (2, 1).

Solve the following system of equations: 3x + 2y = 5 2x - y = 1

  1. (x, y) = (1, 2)

  2. (x, y) = (2, 1)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)


Correct Option: A
Explanation:

To solve this system of equations, we can use the substitution method. Solving the second equation for y, we get y = 2x - 1. Substituting this into the first equation, we get 3x + 2(2x - 1) = 5. Solving for x, we get x = 1. Substituting x = 1 back into the second equation, we get y = 2(1) - 1 = 1. Therefore, the solution is (x, y) = (1, 2).

Solve the following system of equations: 2x + 3y = 7 4x - 2y = 10

  1. (x, y) = (2, 1)

  2. (x, y) = (1, 2)

  3. (x, y) = (3, -1)

  4. (x, y) = (-1, 3)


Correct Option: A
Explanation:

To solve this system of equations, we can use the elimination method. Multiplying the first equation by 2 and the second equation by 3, we get: 4x + 6y = 14 12x - 6y = 30 Adding the two equations, we get: 16x = 44 Solving for x, we get x = 2. Substituting x = 2 back into either of the original equations, we can solve for y. Using the first equation, we get 2(2) + 3y = 7, which gives y = 1. Therefore, the solution is (x, y) = (2, 1).

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