# How do you solve y-6x=22 and 4y+17=-11x using substitution?

May 17, 2018

$x = - 3$
$y = 4$

#### Explanation:

Solving through Substitution

$y - 6 x = 22$
$4 y + 17 = - 11 x$

First, we want to solve for a variable that can be easily found. Then, we'll plug the variable in to solve for the variables. Let's start with finding what y is since it looks easy to solve for.

$y - 6 x = 22$

Add 6x to both sides to negate $- 6 x$. This'll give us $y$'s value. You should now have:

$y = 6 x + 22$

Substitute in this value for y in the second equation to solve for the variables:

$4 y + 17 = - 11 x$
$4 \left(6 x + 22\right) + 17 = - 11 x$

Distribute.

$24 x + 88 + 17 = - 11 x$

Combine like terms. $88 + 17$ is $105$, so:

$24 x + 105 = - 11 x$

Subtract $24 x$ from both sides to negate $24 x$ in order to solve for x. The reason why we aren't adding $11 x$ to both sides is because it'll make the equation unbalanced. $- 11 x - 24 x$ is basically the same as $11 + 24$because they're the same sign, so they combine to become $- 35 x$. So:

$105 = - 35 x$

Divide by -35 to solve for x.

$\frac{105}{-} 35$ = $x$

$x = - 3$

Now, plug this variable back into this equation to solve for y:

$y = 6 x + 22$
$y = 6 \left(- 3\right) + 22$

Distribute.

$y = - 18 + 22$

$y = 4$

Confirm this by plugging it back into the two equations:

$y - 6 x = 22$
$4 - 6 \left(- 3\right) = 22$

Distribute.

$4 + 18 = 22$
$22 = 22$

$4 y + 17 = - 11 x$
4(4) + 17 = -11(-3) 16 + 17 = 33 33 = 33#

Confirmed: these are the correct variables.

May 17, 2018

See a solution process below:

#### Explanation:

Step 1) Solve the first equation for $y$:

$y - 6 x + \textcolor{red}{6 x} = 22 + \textcolor{red}{6 x}$

$y - 0 = 22 + 6 x$

$y = 22 + 6 x$

Step 2) Substitute $\left(22 + 6 x\right)$ for $y$ in the second equation and solve for $x$:

$4 y + 17 = - 11 x$ becomes:

$4 \left(22 + 6 x\right) + 17 = - 11 x$

$\left(4 \cdot 22\right) + \left(4 \cdot 6 x\right) + 17 = - 11 x$

$88 + 24 x + 17 = - 11 x$

$88 + 17 + 24 x = - 11 x$

$105 + 24 x = - 11 x$

$105 - \textcolor{red}{105} + 24 x + \textcolor{b l u e}{11 x} = - 11 x + \textcolor{b l u e}{11 x} - \textcolor{red}{105}$

$0 + \left(24 + \textcolor{b l u e}{11}\right) x = 0 - 105$

$35 x = - 105$

$\frac{35 x}{\textcolor{red}{35}} = - \frac{105}{\textcolor{red}{35}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{35}}} x}{\cancel{\textcolor{red}{35}}} = - 3$

$x = - 3$

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

$y = 22 + 6 x$ becomes:

$y = 22 + \left(6 \times - 3\right)$

$y = 22 - 18$

$y = 4$

The Solution Is:

$x = - 3$ and $y = 4$

Or

$\left(- 3 , 4\right)$