Solve the system by graphing.

x+y=4
-x+y=2

How do I graph this?

solve each for y to make it easy:

y = -x +4
y = x + 2
Now put two points for each line on your graph paper and draw the lines. Note where they cross each other, in this case at right angles at (1,3)

To graph this system of equations, you will need to plot the points that satisfy each equation and find where the lines intersect.

Let's start by graphing the first equation, x + y = 4.

1. Rewrite the equation in slope-intercept form (y = mx + b):
y = -x + 4

2. Choose values for x and solve for y to find points on the line. You can select any values, but it's usually helpful to choose at least two points.
For example, when x = 0, y = -0 + 4 = 4, so one point is (0, 4).
When x = 4, y = -4 + 4 = 0, so another point is (4, 0).

3. Plot the points (0, 4) and (4, 0) on the coordinate plane. Then, draw a straight line passing through these two points. This is the graph of the first equation.

Next, let's graph the second equation, -x + y = 2.

1. Rewrite the equation in slope-intercept form (y = mx + b):
y = x + 2

2. Choose values for x and solve for y to find points on the line.
For example, when x = 0, y = 0 + 2 = 2, so one point is (0, 2).
When x = 4, y = 4 + 2 = 6, so another point is (4, 6).

3. Plot the points (0, 2) and (4, 6) on the coordinate plane. Draw a straight line passing through these points. This is the graph of the second equation.

Now, observe where the two lines intersect. The point of intersection represents the solution to the system of equations. If the lines do not intersect, it means the system has no solution.

In this case, when you graph both equations, you will see that the lines intersect at the point (1, 3). Therefore, the solution to the system is x = 1 and y = 3.