Question

graph the system of equations on the same coordinate grid shown. identify
y = \frac{3}{2}x + 2
y = x - 1

Explanation:

Step1: Find intersection by solving equations

We have the system of equations:
\[

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

\]
Set the two expressions for \(y\) equal to each other:
\(\frac{3}{2}x + 2 = x - 1\)

Step2: Solve for \(x\)

Subtract \(x\) from both sides:
\(\frac{3}{2}x - x+ 2 = - 1\)
\(\frac{1}{2}x+ 2 = - 1\)
Subtract 2 from both sides:
\(\frac{1}{2}x= - 1 - 2\)
\(\frac{1}{2}x= - 3\)
Multiply both sides by 2:
\(x = - 6\)

Step3: Solve for \(y\)

Substitute \(x = - 6\) into \(y = x - 1\):
\(y=-6 - 1=-7\)

Step4: Graph the lines (optional for verification)

• For \(y=\frac{3}{2}x + 2\): When \(x = 0\), \(y = 2\); when \(y = 0\), \(\frac{3}{2}x+2 = 0\Rightarrow x=-\frac{4}{3}\approx - 1.33\)
• For \(y=x - 1\): When \(x = 0\), \(y=-1\); when \(y = 0\), \(x = 1\)

Plot these points and draw the lines. The intersection point is \((-6,-7)\)

Answer:

The solution to the system of equations is \(x=-6\) and \(y = - 7\), so the solution point is \((-6,-7)\)