Answer
$(x, y)= \left(\frac{22}{7},-\frac{94}{7}\right)$ (consistent and independent system)
Work Step by Step
Given: $$\begin{cases}
y &= 4(x-7)+2\\
&= 4x-26\\
y& =-3(x+2)+2\\
&= -3x-4
\end{cases}$$ We are asked to use the method of substitution to solve the given system. Do the substitution and solve: $$\begin{aligned}
4x-26 &= -3x-4\\
4x+3x &=26-4 \\
7x &= 22\\
x&= \frac{22}{7}.\\
y &= -3\cdot\frac{22}{7}-4\\
&=-\frac{66+28}{7} \\
&=-\frac{94}{7}.
\end{aligned}$$ The solution set is $(x, y)= \left(\frac{22}{7},-\frac{94}{7}\right)$ . The system is consistent and independent because it has a single solution.
