Home > CCA2 > Chapter 12 > Lesson 12.1.3 > Problem12-47

12-47.

Solve each system. Homework Help ✎

1. $\left. \begin{array} { l } { \frac { x } { 2 } + \frac { y } { 4 } = 4 } \\ { \frac { x } { 4 } - \frac { 3 y } { 8 } = - 2 } \end{array} \right.$

Multiply both equations by a common denominator to remove the fractions.

$4\left(\frac{x}{2}+\frac{y}{4}\right)=\left(4\right)4$

$8\left(\frac{x}{4}-\frac{3y}{8}\right)=\left(-2\right)8$

$2x+y=16$
$2x-3y=−16$

Solve the new system of equations using the Elimination Method.

$4y=32$, so $y=8$.

Substitute this value back into one of the original equations to solve for $x$.

$(4,8)$

1. $x+2y+z=-1$
$4x-y-z=-1$
$-3y=2z$

Simplify this system of equations using substitution.

Start by solving the third equation for $z$.

$z = \frac{-3y}{2}$

Substitute this value into the first two equations and simplify.

$4x +\frac{y}{2}=-1$

$x + \frac{y}{2}=-1$

You can now solve this equation using the Elimination Method as in part (a).