Question

Fill in the box(es) below to set up the system for ELIMINATION. Then SOLVE the system. (x - 3y = 1) (2x - y = 7)

Answer 1

The equations are x-3y=1 and 2x-y=7.

Multiply the equation 2x-y=7 by 3 to make coefficents of y in both the equation equal.

$\begin{gathered} 3(2x-y)=3\cdot7 \\ 6x-3y=21 \end{gathered}$

Substarct the equation 6x-3y=21 from the equation x-3y=1 to eliminate the y terms from the equation.

$\begin{gathered} x-3y-(6x-3y)=1-21 \\ x-3y-6x+3y=1-21 \\ -5x=-20 \\ x=\frac{-20}{-5} \\ x=4 \end{gathered}$

Substitute 4 for x in equation 2x-y=7 to obtain the value of y.

$\begin{gathered} 2\times4-y=7 \\ 8-y=7 \\ -y=7-8 \\ -y=-1 \\ y=1 \end{gathered}$

So the solution of equation is (4,1).