# How do you solve the following linear system: -x + 4y = -8 , 3x + 2y = 9 ?

Nov 14, 2015

Substitution.

#### Explanation:

Substitution Method
Solve for $x$ in the equation $- x + 4 y = - 8$.

Subtract $4 y$ from both sides: $- x = - 4 y - 8$
Divide both sides by $- 1$: $x = 4 y + 8$
Now, knowing that $x = 4 y + 8$, replace $x$ in the other equation with $4 y + 8$.

This gives: $3 \left(4 y + 8\right) + 2 y = 9$
Distribute: $12 y + 24 + 2 y = 9$
Combine like terms on the left side: $14 y + 24 = 9$
Subtract $24$ from both sides: $14 y = - 15$
Divide both sides by $14$: $\textcolor{red}{y = - \frac{15}{14}}$

Now, plug in your new value for $y$ in either equation.
Example: $3 x + 2 \left(- \frac{15}{14}\right) = 9$
Multiply: $3 x + \left(- \frac{30}{14}\right) = 9$
Simplify: $3 x - \frac{15}{7} = 9$
Add $\frac{15}{7}$ to both sides and find a common denominator: $3 x = \frac{15}{7} + \frac{63}{7}$
Add: $3 x = \frac{78}{7}$
Divide both sides by $3$: $x = \frac{78}{15}$
Simplify: $\textcolor{red}{x = \frac{26}{5}}$