# 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!

Nov 18, 2016

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

#### Explanation:

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

$- 7 x + y + 7 x = - 19 + 7 x$

$y = - 19 + 7 x$

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

$- 2 x + 3 \left(- 19 + 7 x\right) = - 19$

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

$19 x - 57 = - 19$

$19 x - 57 + 57 = - 19 + 57$

$19 x = 38$

$\frac{19 x}{19} = \frac{38}{19}$

$x = 2$

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

$y = - 19 + \left(7 \cdot 2\right)$

$y = - 19 + 14$

$y = - 5$