# How do you solve x=y+4 and x=2y+8 using substitution?

Jul 5, 2017

See a solution process below:

#### Explanation:

Step 1) Because both equations are solve solve for $x$, we substitute $y + 4$ from the first equation for $x$ in the second equation and solve for $y$:

$y + 4 = 2 y + 8$

$- \textcolor{red}{y} + y + 4 - \textcolor{b l u e}{8} = - \textcolor{red}{y} + 2 y + 8 - \textcolor{b l u e}{8}$

$0 - 4 = - \textcolor{red}{1 y} + 2 y + 0$

$- 4 = \left(- \textcolor{red}{1} + 2\right) y$

$- 4 = 1 y$

$- 4 = y$

$y = - 4$

Step 2) Substitute $- 4$ for $y$ in either of the original equations and calculate $x$. I will substitute it into the first equation:

$x = y + 4$ becomes:

$x = - 4 + 4$

$x = 0$

The solution is: $x = 0$ and $y = - 4$ or $\left(0 , - 4\right)$

Jul 5, 2017

Place the value $y + 4$ into the equation $x = 2 y + 8$ and solve for y, then use the value of y to solve for x.

#### Explanation:

$x = y + 4$ so putting this into the second equation gives.

$y + 4 = 2 y + 8$ solve for y by subtracting y and 8 from both sides.

$y - y + 4 - 8 = 2 y - y + 8 - 8$ Which gives

$- 4 = y$ now put -4 into the first equation for solve for x

$x = - 4 + 4$ so

$x = 0$

Jul 5, 2017

$y = - 4 , x = 0$

#### Explanation:

$x = y + 4 - - - - \left(1\right)$

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

substitute color(magenta)(x=y+4  in (1)

$\therefore \left(\textcolor{m a \ge n t a}{y + 4}\right) = 2 y + 8$

$\therefore y - 2 y = 8 - 4$

$\therefore - y = 4$

:.color(magenta)(y=-4

substitute color(magenta)(y=-4 in (1)

$\therefore x = \left(\textcolor{m a \ge n t a}{- 4}\right) + 4$

:.color(magenta)(x=0

substitute $y = - 4$and$x = 0$ in (2)

$\therefore 0 = 2 \left(- 4\right) + 8$

$\therefore 0 = - 8 + 8$

:.color(magenta)(0=0