Question

points to move the lines on the graph. then write the solution as an ordered pair. if no solution exists, write
o solution\; if infinite solutions exist, write \infinite solutions\. \\(\

$$\begin{cases} y = x - 2 \\\\ y = \\frac{3}{2}x - 1 \\end{cases}$$

\\) show your work here

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \( x - 2=\frac{3}{2}x - 1 \)

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( - 2=\frac{3}{2}x - x - 1 \)
Simplify the right side: \( - 2=\frac{1}{2}x - 1 \)
Add 1 to both sides: \( -2 + 1=\frac{1}{2}x \)
Simplify: \( -1=\frac{1}{2}x \)
Multiply both sides by 2: \( x=-2 \)

Step3: Solve for \( y \)

Substitute \( x = - 2 \) into \( y=x - 2 \): \( y=-2 - 2=-4 \)

Answer:

\((-2, - 4)\)