# How do you solve the system 3y=-1/2x+2 and y=-x+9?

Jun 14, 2015

Substitute the expression for $y$ from the second equation into the first and solve for $x$ to get $x = 10$ and $y = - 1$

#### Explanation:

Substitute the expression for $y$ from the second equation into the first...

$- \frac{1}{2} x + 2 = 3 y = 3 \left(- x + 9\right) = - 3 x + 27$

Add $3 x$ to both sides to get:

$\frac{5}{2} x + 2 = 27$

Subtract $2$ from both sides to get:

$\frac{5}{2} x = 25$

Multiply both sides by $\frac{2}{5}$ to get:

$x = 10$

Then $y = - x + 9 = - 10 + 9 = - 1$