Questions: Solve this system of equations by graphing. First gra solution. x-y=7 y=2x-8

Solution Steps

The first equation is \(x - y = 7\). To rewrite this in slope-intercept form (\(y = mx + b\)), we isolate \(y\). Subtract \(x\) from both sides: \(-y = -x + 7\). Multiply both sides by -1: \(y = x - 7\). Now we have the two equations in slope-intercept form: \(y = x - 7\) \(y = 2x - 8\)

For the first equation, \(y = x - 7\), the slope is 1 and the y-intercept is -7.

For the second equation, \(y = 2x - 8\), the slope is 2 and the y-intercept is -8.

The y-intercept of the first equation is -7, so plot the point (0, -7).

The y-intercept of the second equation is -8, so plot the point (0, -8).

For the first equation, the slope is 1. From the y-intercept (0, -7), move 1 unit up and 1 unit right to find the point (1, -6).

For the second equation, the slope is 2. From the y-intercept (0, -8), move 2 units up and 1 unit right to find the point (1, -6).

Notice that both lines pass through the point (1, -6). This means that the lines intersect at (1, -6), which is the solution to the system of equations.

Final Answer