Question

find the solution to the system of equations. you can use the interactive graph below to find the solution. \

$$\begin{cases} y = -2x + 7 \\\\ y = 5x - 7 \\end{cases}$$

x = \boxed{ } y = \boxed{ }

Explanation:

Step1: Set the equations equal

Since both equations equal \( y \), set \( -2x + 7 = 5x - 7 \).

Step2: Solve for \( x \)

Add \( 2x \) to both sides: \( 7 = 7x - 7 \).
Add 7 to both sides: \( 14 = 7x \).
Divide by 7: \( x = 2 \).

Step3: Find \( y \)

Substitute \( x = 2 \) into \( y = -2x + 7 \):
\( y = -2(2) + 7 = -4 + 7 = 3 \).

Answer:

\( x = 2 \)
\( y = 3 \)