Question

solve this system of equations by graphing. first graph the equations, and then type the solution.

$y = \frac{7}{2}x - 3$

$y = -\frac{3}{2}x + 7$

click to select points on the graph.

Explanation:

Step1: Set the equations equal

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

Step2: Combine like terms

Add \( \frac{3}{2}x \) to both sides: \( \frac{7}{2}x + \frac{3}{2}x - 3 = 7 \), which simplifies to \( 5x - 3 = 7 \).

Step3: Solve for \( x \)

Add 3 to both sides: \( 5x = 10 \), then divide by 5: \( x = 2 \).

Step4: Find \( y \)

Substitute \( x = 2 \) into \( y = \frac{7}{2}x - 3 \): \( y = \frac{7}{2}(2) - 3 = 7 - 3 = 4 \).

Answer:

The solution is \( (2, 4) \)