Question

solve the system of linear equations by substitution. enter your answer as an ordered pair if the system has a solution. otherwise, enter \all real numbers\ if it has infinite solutions or
o solution\ if it has no solutions.\\(\

$$\begin{cases}3x + y = 11\\\\-5x - y = -23\\end{cases}$$

\\)

Explanation:

Step1: Solve for y from the first equation

From \(3x + y = 11\), we can isolate \(y\) by subtracting \(3x\) from both sides.
\(y = 11 - 3x\)

Step2: Substitute y into the second equation

Substitute \(y = 11 - 3x\) into \(-5x - y = -23\).
\(-5x-(11 - 3x)=-23\)
Simplify the left - hand side:
\(-5x - 11+3x=-23\)
Combine like terms:
\(-2x-11 = - 23\)

Step3: Solve for x

Add 11 to both sides of the equation \(-2x-11=-23\):
\(-2x=-23 + 11\)
\(-2x=-12\)
Divide both sides by \(-2\):
\(x=\frac{-12}{-2}=6\)

Step4: Solve for y

Substitute \(x = 6\) into \(y = 11-3x\):
\(y=11-3\times6\)
\(y=11 - 18=-7\)

Answer:

\((6,-7)\)