Question

Graph the linear system below. Then decide if the ordered pair is a solution of the system. $$ \begin{array}{l} -x+y=-2 \\ 2 x+y=10 \end{array} $$ $$ (-4,-2) $$

Short answer

The ordered pair (-4, -2) is not a solution to the system of equations.

Step-by-step solution

Convert Equations to slope-intercept form

The first equation in slope-intercept form will be \( y = x - 2 \). Similarly, the second equation will be \( y = 10 -2x \).

Graph the Equations

Now, we shall plot the lines on the same graph. For the first line, choose the y-intercept (0, -2) and plot another point by moving one unit right and one unit down (since the slope is 1). For the second line, choose y-intercept (0, 10) and plot another point by moving two units right and one unit down (since the slope is -2).

Substitute Ordered Pair into Equations

Substitute (-4, -2) into both the equations of the system:- For first Equation, \( -2 = -4 - 2 \), which isn't valid as LHS and RHS don't match. Thus, (-4, -2) isn't a solution for this system.