Step By Step 1 of 3 You were asked to solve the following system of linear equations by graphing: \[ \begin{aligned}-4 x+2 y & =14 \\ -x+y & =2\end{aligned} \]

To solve the system of equations by graphing, start by rearranging both equations into slope-intercept form (y = mx + b). For the first equation, \(-4x + 2y = 14\), solve for y: \(2y = 4x + 14\) then \(y = 2x + 7\). For the second equation, \(-x + y = 2\), solve for y: \(y = x + 2\). Now, plot both lines on a graph. The first line has a slope of 2 and a y-intercept of 7, while the second line has a slope of 1 and a y-intercept of 2. Where the lines intersect is the solution to the system of equations! To plot accurately, find points by substituting values for x in both equations. For the first equation, if \(x = 0\), \(y = 7\) making the point (0, 7). For \(x = 1\), \(y = 9\) giving point (1, 9). For the second equation, \(x = 0\) yields point (0, 2) and \(x = 2\) makes \(y = 4\), point (2, 4). Drawing these points will show where the lines intersect, which is your solution!