Question

- Use elimination to solve the system of equations. Select the correct answer and show your

work.
3x - 2y = 24
x + 2y = 48
a) x = 18, y = 15
c) x = 15, y = 10
b) x = 10, y = 3
d) x = 5, y = -2

Answer 1

A

Explanation:

x + 2y = 48 => 2y = 48 - x

3x - (48 - x) = 24

4x - 48 = 24

4x = 72

x = 18

y = 48 - x / 2 = 30/2 = 15

Answer 2

To eliminate y, we can add the two equations:

(3x - 2y) + (x + 2y) = 24 + 48

Simplifying, we get:

4x = 72

Dividing both sides by 4, we get:

x = 18

Now that we know x, we can substitute it into one of the original equations to solve for y. Let's use the second equation:

x + 2y = 48

Substituting x = 18, we get:

18 + 2y = 48

Subtracting 18 from both sides, we get:

2y = 30

Dividing both sides by 2, we get:

y = 15

Therefore, the solution is x = 18, y = 15. The correct answer is (a).