Question

\

$$\begin{cases} y = \\frac{6}{5}x + 3 \\ y = -\\frac{1}{5}x - 4 \\end{cases}$$

show your work here

draw

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other:
\( \frac{6}{5}x + 3 = -\frac{1}{5}x - 4 \)

Step2: Add \( \frac{1}{5}x \) to both sides

To get all the \( x \) terms on one side, we add \( \frac{1}{5}x \) to both sides:
\( \frac{6}{5}x + \frac{1}{5}x + 3 = - 4 \)
\( \frac{7}{5}x + 3 = - 4 \)

Step3: Subtract 3 from both sides

Subtract 3 from both sides to isolate the term with \( x \):
\( \frac{7}{5}x = - 4 - 3 \)
\( \frac{7}{5}x = - 7 \)

Step4: Solve for \( x \)

Multiply both sides by \( \frac{5}{7} \) to solve for \( x \):
\( x = - 7 \times \frac{5}{7} \)
\( x = - 5 \)

Step5: Substitute \( x = - 5 \) into one of the original equations

Let's use the first equation \( y = \frac{6}{5}x + 3 \). Substitute \( x = - 5 \):
\( y = \frac{6}{5}(-5) + 3 \)
\( y = - 6 + 3 \)
\( y = - 3 \)

Answer:

The solution to the system of equations is \( x = - 5 \) and \( y = - 3 \), or the ordered pair \( (-5, -3) \).