# How do you solve the system 2x+7y=8 and x+5y=7 using substitution?

Jun 7, 2015

$x = - 3$ and $y = 2$.

Solve $x + 5 y = 7$ for $x$.

$x = 7 - 5 y$

Substitute $7 - 5 y$ for $x$ into the other equation.

$2 \left(7 - 5 y\right) + 7 y = 8$ =

$14 - 10 y + 7 y = 8$ '

$14 - 3 y = 8$

Subtract $14$ from both sides.

$- 3 y = - 6$

Divide both sides by $- 3$.

$y = 2$

Substitute $2$ for $y$ in the first equation.

$x + 5 \left(2\right) = 7$ =

$x + 10 = 7$

Subtract $10$ from both sides.

$x = - 3$

Check by substituting $- 3$ for $x$ and $2$ for $y$ into both equations.

$2 x + 7 y = 8$ =

$2 \left(- 3\right) + 7 \left(2\right) = 8$ =

$- 6 + 14 = 8$ =

$8 = 8$ Check.

$x + 5 y = 7$ =

$- 3 + 5 \left(2\right) = 7$ =

$- 3 + 10 = 7$ =

$7 = 7$ Check.