Question

the two graphed lines are represented by the system of equations shown, solve the system of equations. \\(\

$$\begin{cases} y = -5 \\\\ 3x - y = -13 \\end{cases}$$

\\) a variable is dual in one equation, and the other equation has the same variable. the substitution method is the way to go 1. write a new equation in a single variable. substitute the value of \\(\boxed{}\\), which is \\(\boxed{}\\), into the equation \\(\boxed{}\\) 2. solve for one variable. 3. solve for the other variable.

Explanation:

Step1: Substitute \( y \) into the second equation

We know from the first equation \( y = -5 \). Substitute \( y = -5 \) into the second equation \( 3x - y = -13 \). So the new equation is \( 3x - (-5) = -13 \), which simplifies to \( 3x + 5 = -13 \).

Step2: Solve for \( x \)

Subtract 5 from both sides of the equation \( 3x + 5 = -13 \):
\( 3x + 5 - 5 = -13 - 5 \)
\( 3x = -18 \)
Divide both sides by 3:
\( x = \frac{-18}{3} = -6 \)

Step3: Solve for \( y \)

From the first equation, we already know \( y = -5 \).

Answer:

The solution to the system of equations is \( x = -6 \) and \( y = -5 \), or the ordered pair \( (-6, -5) \).