Question

2x - 2y = 6
3x + 2y = 9

Answer 1

To solve this system of equations, we can use the method of elimination.

We start by multiplying the first equation by 3 and the second equation by 2 in order to eliminate the y terms.

3(2x - 2y) = 3(6)
2(3x + 2y) = 2(9)

This simplifies to:
6x - 6y = 18
6x + 4y = 18

Next, we subtract the equations to eliminate the x terms.

(6x - 6y) - (6x + 4y) = 18 - 18

Simplifying gives:
-10y = 0

Dividing by -10, we have:
y = 0

Now, we substitute this value of y into one of the original equations and solve for x. Let's use the first equation:

2x - 2(0) = 6
2x = 6
x = 3

Therefore, the solution to the system of equations is x = 3 and y = 0.