Question

solve the system of equations by graphing. \

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

(3,5) (5,3) (6,7) (4,7)

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we set \( \frac{2}{3}x + 3 = 2x - 1 \).

Step2: Solve for \( x \)

Subtract \( \frac{2}{3}x \) from both sides: \( 3 = \frac{4}{3}x - 1 \).
Add 1 to both sides: \( 4 = \frac{4}{3}x \).
Multiply both sides by \( \frac{3}{4} \): \( x = 3 \).

Step3: Find \( y \)

Substitute \( x = 3 \) into \( y = 2x - 1 \): \( y = 2(3) - 1 = 5 \).

Answer:

The solution to the system is \( (3, 5) \)