# How do you solve the system 5x= -25+5y and 10y=42+2x?

Jun 13, 2015

Divide the first equation by $5$ to get an expression for $x$ to substitute in the second equation. Solve to find $y = 4$ and hence $x = - 1$

#### Explanation:

Divide both sides of the first equation by $5$ to get:

$x = - 5 + y = y - 5$

Substitute $y - 5$ for $x$ in the second equation:

$10 y = 42 + 2 x = 42 + 2 \left(y - 5\right)$

$= 42 + 2 y - 10 = 32 + 2 y$

Subtract $2 y$ from both ends to get:

$8 y = 32$

Divide both sides by $8$ to get:

$y = 4$

Then

$x = y - 5 = 4 - 5 = - 1$