Solve each system of equations by graphing.y = 2x + 1y = -x + 1x + y = 4x + y = 2

Sure, let's solve these systems of equations step by step.

1. y = 2x + 1 and y = -x + 1

First, let's graph these two equations. The first equation is a straight line with a slope of 2 and y-intercept of 1. The second equation is a straight line with a slope of -1 and y-intercept of 1.

When you graph these two lines, you'll find that they intersect at the point (0,1). So, the solution to this system of equations is x = 0 and y = 1.

2. x + y = 4 and x + y = 2

Let's graph these two equations. Both are straight lines with a slope of -1. The first line has a y-intercept of 4 and the second line has a y-intercept of 2.

However, when you graph these two lines, you'll find that they are parallel and do not intersect. This means that there is no solution to this system of equations.