# How do you solve –4x + 7y = –10 and x – 5y = 9 using substitution?

Feb 4, 2017

See the entire solution process below:

#### Explanation:

Step 1) Solve the second equation for $x$:

$x - 5 y = 9$

$x - 5 y + \textcolor{red}{5 y} = 9 + \textcolor{red}{5 y}$

$x - 0 = 9 + 5 y$

$x = 9 + 5 y$

Step 2) Substitute $9 + 5 y$ for $x$ in the first equation and solve for $y$:

$- 4 x + 7 y = - 10$

$- 4 \left(9 + 5 y\right) + 7 y = - 10$

$- 36 - 20 y + 7 y = - 10$

$- 36 - 13 y = - 10$

$\textcolor{red}{36} - 36 - 13 y = \textcolor{red}{36} - 10$

$0 - 13 y = 26$

$- 13 y = 26$

$\frac{- 13 y}{\textcolor{red}{- 13}} = \frac{26}{\textcolor{red}{- 13}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 13}}} y}{\cancel{\textcolor{red}{- 13}}} = - 2$

$y = - 2$

Step 3) Substitute $- 2$ for $y$ in the solution to the second equation at the end of Step 1 and calculate $x$:

$x = 9 + 5 y$

$x = 9 + \left(5 \times - 2\right)$

$x = 9 - 10$

$x = - 1$

The solution is $x = - 1$ and $y = - 2$

Feb 4, 2017

$x = - 1$ and $y = - 2$

#### Explanation:

$- 4 x + 7 y = - 10$
$x - 5 y = 9$

Using the second equation, we determine a value for $x$.

$x - 5 y = 9$

Add $5 y$ to each side.

$x = 9 + 5 y$

In the first equation, substitute $x$ with $\textcolor{red}{\left(9 + 5 y\right)}$.

$- 4 x + 7 y = - 10$

$- 4 \textcolor{red}{\left(9 + 5 y\right)} + 7 y = - 10$

Open the brackets and simplify. The product of a negative and a positive is a negative.

$\textcolor{red}{- 36 - 20 y} + 7 y = - 10$

$- 36 - 13 y = - 10$

Add $36$ to both sides.

$- 13 y = 26$

Divide both sides by $- 13$.

$y = - 2$

In the second equation, substitute $y$ with $\textcolor{b l u e}{- 2}$.

$x - 5 \textcolor{b l u e}{\left(- 2\right)} = 9$

Open the brackets and simplify. The product of two negatives is a positive.

$x + 10 = 9$

Subtract $10$ from both sides.

$x = - 1$