Question

solve the system of equations graphed on the coordinate axes below.
y = -3x - 2
y = \frac{3}{2}x + 7

Explanation:

Step1: Set the two equations equal

Since both expressions equal \(y\), we set \(-3x - 2=\frac{3}{2}x+7\).

Step2: Move \(x\) - terms to one side

Add \(3x\) to both sides: \(- 2=\frac{3}{2}x + 3x+7\). Combine like - terms: \(-2=\frac{3x + 6x}{2}+7\), so \(-2=\frac{9x}{2}+7\).

Step3: Move the constant to the other side

Subtract 7 from both sides: \(-2 - 7=\frac{9x}{2}\), which gives \(-9=\frac{9x}{2}\).

Step4: Solve for \(x\)

Multiply both sides by \(\frac{2}{9}\): \(x=-9\times\frac{2}{9}=-2\).

Step5: Find \(y\)

Substitute \(x = - 2\) into \(y=-3x - 2\). Then \(y=-3\times(-2)-2=6 - 2 = 4\).

Answer:

\(x=-2,y = 4\)