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. \\(\

$$\begin{cases} y = -3x + 8 \\\\ 5x + 2y = 15 \\end{cases}$$

\\)

Explanation:

Step1: Substitute \( y = -3x + 8 \) into the second equation

We have the second equation \( 5x + 2y = 15 \). Substitute \( y \) with \( -3x + 8 \), so we get \( 5x + 2(-3x + 8) = 15 \).

Step2: Simplify and solve for \( x \)

First, expand the equation: \( 5x - 6x + 16 = 15 \). Then combine like terms: \( -x + 16 = 15 \). Subtract 16 from both sides: \( -x = 15 - 16 = -1 \). Multiply both sides by -1: \( x = 1 \).

Step3: Substitute \( x = 1 \) back to find \( y \)

Substitute \( x = 1 \) into \( y = -3x + 8 \), so \( y = -3(1) + 8 = -3 + 8 = 5 \).

Answer:

\((1, 5)\)