Question

1. the graph on the coordinate plane represents the given system. verify algebraically that the ordered pair (-2, 8) satisfies the system of equations. \\(\

$$\begin{cases} y = -2x + 3 \\\\ y = \\frac{1}{2}x + 8 \\end{cases}$$

\\)

Explanation:

Step1: Check first equation

Substitute \( x = -2 \) and \( y = 6 \) into \( y = -2x + 2 \).
Right - hand side: \( -2\times(-2)+2=4 + 2=6 \), which equals \( y = 6 \).

Step2: Check second equation

Substitute \( x=-2 \) and \( y = 6 \) into \( y=\frac{1}{2}x + 7 \).
Right - hand side: \( \frac{1}{2}\times(-2)+7=-1 + 7 = 6 \), which equals \( y = 6 \).

Answer:

Since the ordered pair \((-2,6)\) satisfies both equations \(y=-2x + 2\) and \(y=\frac{1}{2}x+7\), it is a solution to the system of equations.