Question

is (7, -1) a solution to the following system of equations? \

$$\begin{cases} -2x - 6y = -8 \\\\ x - 4y = 11 \\end{cases}$$

Explanation:

Step1: Check first equation

Substitute \(x = 7\), \(y=-1\) into \(-2x - 6y\):
\(-2(7)-6(-1)=-14 + 6=-8\), which matches the right - hand side of the first equation \(-2x - 6y=-8\).

Step2: Check second equation

Substitute \(x = 7\), \(y = - 1\) into \(x-4y\):
\(7-4(-1)=7 + 4 = 11\), which matches the right - hand side of the second equation \(x - 4y=11\).

Answer:

Yes, \((7,-1)\) is a solution to the system of equations.