Question

Solve the system of equations using elimination: 3x-2y=2 and 2x-5y=27

Answer 1

(-4,-7)

Explanation:

Multiply both sides of the first equation by-5 or 2 (I'll use 5) and both sides of the second equation by - 2 or 3 (I'll use -2).

3x - 2y = 2

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

-15x - 10y = 10

2x - 5y = 27

-2(2x - 5y) = -2(27)

-4x + 10y = -54

Now you see that the absolute values of the y-values of the 2 equations match up . They are still the same equations but scaled up.

-15x + 10y = 10

-4x - 10y = -54

Add to eliminate y.

-11x = 44

Divide both sides by -11.

`(-11x)/(-11) = (44)/(-11)`

x = -4

Plug back in to either equation to solve. I'll use the first equation.

3x - 2y = 2

x = - 4

3(-4) - 2y = 2

-12 - 2y = 2

Add 12 on both sides.

-12 + 12 - 2y = 2 + 12

- 2y = 14

Divide -2y on both sides.

`(-2y)/(-2) = (14)/(-2)`

y = -7

(-4,-7)