# How do you solve the system of equations by graphing 8x + 5y = -3 and -2x + y = 21 and then classify the system?

Jun 4, 2018

$x = - 6$
$y = 9$

#### Explanation:

$8 x + 5 y = - 3$
$- 2 x + y = 21$

Solving by Substitution

First, we're going to find an equation for the value of a variable to plug it into the other equation in the system. $- 2 x + y = 21$ looks like it can easily be rearranged to get the equation for the value of $y$.

$- 2 x + y = 21$

Add $2 x$ to both sides to isolate for the equation for the value of $y$. You should now have:

$y = 2 x + 21$

Now that you have the equation for the value of $y$, you can plug the terms $\left(2 x + 21\right)$ into where $y$ would appear in the other equation of the system. So:

$8 x + 5 y = - 3$
$8 x + 5 \left(2 x + 21\right) = - 3$

Distribute. What this means is that you'll be multiplying $2 x$ by $5$ and $21$ by $5$. So:

$5 \cdot 2 x = 10 x$
$5 \cdot 21 = 105$

Re-write the equation:

$8 x + 10 x + 105 = - 3$
Combine like terms $\left(10 x + 8 = 18 x\right)$:

$18 x + 105 = - 3$

This is a two-step equation. Subtract $105$ from both sides to cancel out $105$ in order to get closer to finding the value of $x$.

$18 x = - 108$

Divide by $18$ to isolate for $x$:

$- \frac{108}{18} = x$

$- \frac{108}{18} = - 6$

$x = - 6$

Plug the value of $x$ back into the equation for the value of $y$ to figure out $y$'s value:

$y = 2 x + 21$
$y = 2 \left(- 6\right) + 21$
$y = - 12 + 21$
$y = 9$

Plug these values back into the whole system to prove they're right:

$8 x + 5 y = - 3$
$8 \left(- 6\right) + 5 \left(9\right) = - 3$
$- 48 + 45 = - 3$
$- 3 = - 3$

$- 2 x + y = 21$
$- 2 \left(- 6\right) + 9 = 21$
$12 + 9 = 21$
$21 = 21$

These are the correct values.