Question

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

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

\\) \\(x = \square\\) \\(y = \square\\) (graph with coordinate plane and a horizontal line, green dots at y=4)

Explanation:

Step1: Set equations equal

Since \( y = -2x + 7 \) and \( y = 5x - 7 \), 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:

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