Question

How do I find the solution to the problem -7x+y= -19 and -2x+3y= -19?

I need to find a solution for this problem using the method of elimination.
Thanks!

Answer 1

`x = 2` and `y = -5`

Explanation:

Step 1) Solve the first equation for `y` while keeping the equation balanced:

`-7x + y + 7x = -19 + 7x`

`y = -19 + 7x`

Step 2) Substitute `-19 + 7x` for `y` in the second equation and solve for `x` while keeping the equation balanced:

`-2x + 3(-19 + 7x) = -19`

`-2x - 57 + 21x = -19`

`19x - 57 = - 19`

`19x - 57 + 57 = -19 + 57`

`19x = 38`

`(19x)/19 = 38/19`

`x = 2`

Step 3) Substitute `2` for `x` in the first equation and calculate `y`:

`y = -19 + (7*2)`

`y = -19 + 14`

`y = -5`