Question

Given the following system of equations, identify the type of system.x + y = 4x - y = 6consistentinconsistentequivalent

Answer 1

$\begin{gathered} x+y=4_{\text{ }}(1) \\ x-y=6_{\text{ }}(2) \end{gathered}$

Using elimination method:

$\begin{gathered} (1)+(2) \\ x+x+y-y=4+6 \\ 2x=10 \\ x=\frac{10}{2} \\ x=5 \\ so\colon \\ y=4-5 \\ y=-1 \end{gathered}$

Since the system has a unique solution, we can conclude it is a consistent system