How do you solve the following system?: 4x -12y =-3 , -3x +y = 18

Jan 15, 2017

See entire solution process below:

Explanation:

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

$- 3 x + y = 18$

$- 3 x + \textcolor{red}{3 x} + y = 18 + \textcolor{red}{3 x}$

$0 + y = 18 + 3 x$

$y = 3 x + 18$

Step 2) Substitute $3 x + 18$ for $y$ in the first equation and solve for $x$:

$4 x - 12 y = - 3$

$4 x - 12 \left(3 x + 18\right) = - 3$

$4 x - 36 x - 216 = - 3$

$- 32 x - 216 = - 3$

$- 32 x - 216 + \textcolor{red}{216} = - 3 + \textcolor{red}{216}$

$- 32 x - 0 = 213$

$- 32 x = 213$

$\frac{- 32 x}{\textcolor{red}{- 32}} = \frac{213}{\textcolor{red}{- 32}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 32}}} x}{\cancel{\textcolor{red}{- 32}}} = - 6.65625$

$x = - 6.65625$

Step 3) Substitute $- 6.65625$ for $x$ into the solution for $y$ in the second equation in Step 1 and calculate $y$:

$y = 3 x + 18$

$y = \left(3 \times - 6.65625\right) + 18$

$y = - 19.96875 + 18$

$y = - 1.96875$

The solution is: $x = - 6.65625$ and $y = - 1.96875$