# Question #bbb03

Dec 15, 2017

You solve this as a systems of equations.

#### Explanation:

Start by multiplying the entire equation of $y = 4 x - 7$ by $7$ and the entire equation of $y = - 7 x + 15$ by $4$. Now you have:

$7 y = 28 x - 49 \text{ }$ and $\text{ } 4 y = - 28 x + 60$

Line them up vertically:

$7 y = 28 x - 49$
$4 y = - 28 x + 60$

and subtract them, so the $x$'s cancel out. You now should have

$3 y = 11$

Divide both sides by $3$ to get $y$ by itself, and you get

$y = \frac{11}{3.}$

Now, plug in $\frac{11}{3}$ for $y$ into the original equation and solve for $x$:

$\frac{11}{3} = 4 x - 7 \text{ }$ (add $7$ to both sides to cancel it)

$\frac{32}{3} = 4 x \text{ }$ (divide both sides by $4$ to cancel it)

$\frac{8}{3} = x$

BAM! You're done!

Dec 15, 2017

$x = 2 \mathmr{and} y = 1$

#### Explanation:

This is the best form to have when solving a system of equations,!

They both show $y$ in terms of $x$.

We know that $\textcolor{red}{y = y}$

So, the expressions that are both equal to $y$ must be equal!

$\textcolor{w h i t e}{\times \times} \textcolor{red}{y = y}$

$\textcolor{red}{4 x - 7 = - 7 x + 15} \text{ } \leftarrow$ solve for $x$

$4 x + 7 x = 15 + 7$

$11 x = 22$

$x = 2$

Substitute $2$ for $x$ in both equations to check that you get the same answer.

$y = 4 x - 7 \text{ "and" } y = - 7 x + 15$

$y = 4 \left(2\right) - 7 \text{ "and" } y = - 7 \left(2\right) + 15$

$y = 8 - 7 \text{ "and " } y = - 14 + 15$

In both cases $y = 1$