# How do you solve the system y = 4x - 3 and y = - 3x - 3 by graphing?

Dec 24, 2016

$x = 0$ and $y = - 3$

#### Explanation:

Because the second equation has already be solved for $y$ we can substitute $\textcolor{red}{- 3 x - 3}$ for $y$ in the first equation and solve for $x$:

$\textcolor{red}{- 3 x - 3} = 4 x - 3$

$\textcolor{red}{- 3 x - 3} + \textcolor{b l u e}{3 x + 3} = 4 x - 3 + \textcolor{b l u e}{3 x + 3}$

$\textcolor{red}{- 3 x} + \textcolor{b l u e}{3 x} - \textcolor{red}{3} + \textcolor{b l u e}{3} = 4 x + \textcolor{b l u e}{3 x} - 3 + \textcolor{b l u e}{3}$

$0 - 0 = 4 x + \textcolor{b l u e}{3 x} - 0$

$0 = 4 x + \textcolor{b l u e}{3 x}$

$0 = \left(4 + 3\right) x$

$0 = 7 x$

$\frac{0}{\textcolor{red}{7}} = \frac{7 x}{\textcolor{red}{7}}$

$0 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} x}{\cancel{\textcolor{red}{7}}}$

$0 = x$ or $x = 0$

Now that we have $x$ we can substitute $0$ for $x$ in the second equation and calculate $y$:

$y = \left(- 3 \cdot 0\right) - 3$

$y = 0 - 3$

$y = - 3$