# How do you solve the system 2x-3y=-24 and x+6y=18 using substitution?

Jul 15, 2017

See a solution process below:

#### Explanation:

Step 1) Solve the second equation for $x$:

$x + 6 y = 18$

$x + 6 y - \textcolor{red}{6 y} = 18 - \textcolor{red}{6 y}$

$x + 0 = 18 - 6 y$

$x = 18 - 6 y$

Step 2) Substitute $\left(18 - 6 y\right)$ for $x$ in the first equation and solve for $y$:

$2 x - 3 y = - 24$ becomes:

$2 \left(18 - 6 y\right) - 3 y = - 24$

$\left(2 \times 18\right) - \left(2 \times 6 y\right) - 3 y = - 24$

$36 - 12 y - 3 y = - 24$

$36 + \left(- 12 - 3\right) y = - 24$

$36 + \left(- 15 y\right) = - 24$

$36 - 15 y = - 24$

$- \textcolor{red}{36} + 36 - 15 y = - \textcolor{red}{36} - 24$

$0 - 15 y = - 60$

$- 15 y = - 60$

$\frac{- 15 y}{\textcolor{red}{- 15}} = \frac{- 60}{\textcolor{red}{- 15}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 15}}} y}{\cancel{\textcolor{red}{- 15}}} = 4$

$y = 4$

Step 3) Substitute $4$ for $y$ in the solution to the second equation at the end of Step 1 and calculate $x$:

$x = 18 - 6 y$ becomes:

$x = 18 - \left(6 \cdot 4\right)$

$x = 18 - 24$

$x = - 6$

The solution is: $x = - 6$ and $y = 4$ or $\left(- 6 , 4\right)$

Jul 15, 2017

color(blue)(y=4,x=-6

#### Explanation:

$\therefore 2 x - 3 y = - 24 - - - - \left(1\right)$

$x + 6 y = 18 - - - - \left(2\right)$
:.
in (2) $x = 18 - 6 y$

substitute color(blue)(x=18-6y in (1)

$\therefore 2 \left(\textcolor{b l u e}{18 - 6 y}\right) - 3 y = - 24$

$\therefore 36 - 12 y - 3 y = - 24$

$\therefore - 15 y = - 24 - 36$

multiply both sides by$- 1$

$\therefore 15 y = 24 + 36$

$\therefore 15 y = 60$

:.color(blue)(y=4

substitute color(blue)(y=4  in (2)

$\therefore x + 6 \left(\textcolor{b l u e}{4}\right) = 18$

$\therefore x + 24 = 18$

$\therefore x = 18 - 24$

:.color(blue)(x=-6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

color(blue)(check:

substitute color(blue)(y=4 andcolor(blue)(x=-6 in (2)

:.(color(blue)(-6))+6(color(blue)(4))=18))

$\therefore - 6 + 24 = 18$

:.color(blue)(18=18