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

Question

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

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Answer 1 · 2016-11-18T15:40:01

$x = 2$ and $y = -5$

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 $y$ :

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

$y = -19 + 14$

$y = -5$