Question

graph the systems of equations below, then place a point indicating the solution to the system of equations. \\(\

$$\begin{cases} y = -\\frac{1}{2}x - 1 \\\\ y = \\frac{1}{4}x - 4 \\end{cases}$$

\\)

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we set \( -\frac{1}{2}x - 1=\frac{1}{4}x - 4 \)

Step2: Solve for \( x \)

Add \( \frac{1}{2}x \) to both sides: \( - 1=\frac{1}{4}x+\frac{1}{2}x - 4 \)
Simplify the \( x \)-terms: \( - 1=\frac{3}{4}x - 4 \)
Add 4 to both sides: \( 3=\frac{3}{4}x \)
Multiply both sides by \( \frac{4}{3} \): \( x = 4 \)

Step3: Find \( y \)

Substitute \( x = 4 \) into \( y=\frac{1}{4}x - 4 \): \( y=\frac{1}{4}(4)-4=1 - 4=-3 \)

Answer:

The solution to the system of equations is the point \( (4, - 3) \)