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.\\(\

$$\begin{cases} y = -x + 2 \\\\ 5x + 2y = -5 \\end{cases}$$

\\)

Explanation:

Step1: Substitute \( y = -x + 2 \) into the second equation

We have the second equation \( 5x + 2y = -5 \). Substitute \( y \) with \( -x + 2 \), so we get \( 5x + 2(-x + 2) = -5 \).

Step2: Simplify and solve for \( x \)

First, expand the left - hand side: \( 5x-2x + 4=-5 \). Combine like terms: \( 3x+4 = - 5 \). Subtract 4 from both sides: \( 3x=-5 - 4=-9 \). Then divide both sides by 3: \( x=\frac{-9}{3}=-3 \).

Step3: Substitute \( x = - 3 \) into \( y=-x + 2 \) to find \( y \)

Substitute \( x=-3 \) into \( y=-x + 2 \), we have \( y=-(-3)+2=3 + 2 = 5 \).

Answer:

\((-3,5)\)