Question

two systems of equations are given below. for each system, choose the best description of its solution. if applicable, give the solution.

Answer 1

Let:

$\begin{gathered} x-4y=8_{\text{ }}(1) \\ -x-4y=8_{\text{ }}(2) \\ \end{gathered}$

Using elimination method:

$\begin{gathered} (1)+(2) \\ x+(-x)+(-4y)+(-4y)=8+8 \\ -8y=16 \\ y=\frac{16}{-8} \\ y=-2 \end{gathered}$

Replace the value of y into (1):

$\begin{gathered} x-4(-2)=8 \\ x+8=8 \\ x=8-8 \\ x=0 \end{gathered}$

The system has unique solution:

$(x,y)=(0,-2)$