Question

1. the graph on the coordinate plane represents the given system. verify algebraically that the ordered pair $(-2, 5)$ satisfies the system of equations.\\\

$$\begin{cases} y = -2x + 1 \\\\ y = \\frac{1}{2}x + 6 \\end{cases}$$

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• choose the correct answer -

Explanation:

Step1: Verify first equation \( y = -2x + 1 \)

Substitute \( x = -2 \) and \( y = 5 \) into the equation:
Right - hand side (RHS) \(=-2\times(-2)+1 = 4 + 1=5\)
Left - hand side (LHS) \(= y = 5\)
Since LHS = RHS, the ordered pair satisfies the first equation.

Step2: Verify second equation \( y=\frac{1}{2}x + 6 \)

Substitute \( x=-2 \) and \( y = 5 \) into the equation:
Right - hand side (RHS) \(=\frac{1}{2}\times(-2)+6=-1 + 6 = 5\)
Left - hand side (LHS) \(=y = 5\)
Since LHS = RHS, the ordered pair satisfies the second equation.

Answer:

The ordered pair \((-2,5)\) satisfies both equations \(y = - 2x+1\) and \(y=\frac{1}{2}x + 6\) because when \(x=-2\) and \(y = 5\) are substituted into each equation, the left - hand side equals the right - hand side for both equations.