Question

HELP

8.
Which ordered pair is the solution of the following
system of equations?
3x + 2y = 4
–2x + 2y = 24
A. (2, -1)
B. (2,-5)
C. (-4,8)
D. (-4,-8)

Answer 1

C. (-4,8). To find the solution to the system of equations, use the elimination method. The correct answer is (x, y) = (-4, 8).

Step-by-step explanation:

To find the solution to the system of equations, we can use the method of substitution or elimination. Let's use the elimination method:

1. Multiply the second equation by 3 to get rid of the y coefficient: -6x + 6y = 72
2. Add the two equations together: (3x + 2y) + (-6x + 6y) = 4 + 72
3. Simplify: -3x + 8y = 76
4. Now we have a new equation: -3x + 8y = 76
5. Multiply the first equation by -4 to get rid of the x coefficient: -12x - 8y = -16
6. Add the two equations together: (-3x + 8y) + (-12x - 8y) = 76 + (-16)
7. Simplify: -15x = 60
8. Divide both sides by -15: x = -4
9. Substitute x = -4 into the first equation to find y: 3(-4) + 2y = 4
10. Simplify: -12 + 2y = 4
11. Add 12 to both sides: 2y = 16
12. Divide both sides by 2: y = 8

The solution to the system of equations is (x, y) = (-4, 8). Therefore, the correct answer is C. (-4, 8).

Answer 2

C

Step-by-step explanation:

Given the 2 equations

3x + 2y = 4 → (1)

- 2x + 2y = 24 → (2)

Multiplying (2) by - 1 and adding to (1) will eliminate the y- term

2x - 2y = - 24 → (3)

Add (1) and (3) term by term to eliminate y

5x + 0 = - 20

5x = - 20 ( divide both sides by 5 )

x = - 4

Substitute x = - 4 into either of the 2 equations and solve for y

Substituting into (1)

3(- 4) + 2y = 4

- 12 + 2y = 4 ( add 12 to both sides )

2y = 16 ( divide both sides by 2 )

y = 8

solution is (- 4, 8 ) → C