Question

Solve the following using Elimination
3x-2y=2
-5x+5y=-10

Answer 1

To solve this system of equations using elimination, we can multiply the first equation by 5 and the second equation by 2 to make the coefficients of the y term opposite.

5(3x - 2y) = 5(2)
2(-5x + 5y) = 2(-10)

Simplifying, we get:

15x - 10y = 10
-10x + 10y = -20

Next, we can add the two equations together to eliminate the y term:

(15x - 10y) + (-10x + 10y) = 10 + (-20)

Simplifying, we get:

15x - 10x - 10y + 10y = -10

Combining like terms, we get:

5x = -10

Dividing both sides of the equation by 5, we find:

x = -2

To find the value of y, we can substitute the value of x into one of the original equations:

3(-2) - 2y = 2

Simplifying, we have:

-6 - 2y = 2

Adding 6 to both sides, we find:

-2y = 8

Dividing both sides of the equation by -2, we get:

y = -4

Therefore, the solution to the system of equations is x = -2 and y = -4.