SOLUTION: Solve the system by graphing. x + y = 4 �x + y = 2

Question 81753: Solve the system by graphing.
x + y = 4
�x + y = 2

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.
+x + y = 4
�x + y = 2
.
To solve by graphing, let's look at how to graph the two equations.
.
You can easily find a couple of points on the graph of the top equation by first setting
x equal to zero and solving for y and then by setting y equal to zero and solving for x.
.
Let's do that. In the equation +x + y = 4 when you set x equal to zero, the equation
reduces to y = +4. Therefore, the point (0, 4) is on the graph. Next in the equation
set y equal to zero and the equation reduces to x = 4. This means that the point (4, 0)
is also on the graph of this equation. Plot these two points, and with a straight edge
extend a line through these two points.
.
Next, let's graph the second equation -x + y = 2 by using the same technique. Set x
equal to zero and the equation reduces to y = 2. This means that the point (0, 2) is on
the graph of this equation. Then return to the equation and set y equal to zero. This
reduces the equation to -x = 2, and by multiplying both sides by -1 you get x = -2. Therefore,
the point (-2, 0) is also on this graph. Plot the two points (0, 2) and (-2, 0) and use
a straight edge to extend a line through these two points.
.
Now look for the point where the two graphs cross. The x and y values of this point
are the values that satisfy both of the equations because they are on both graphs.
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Your graphs should look like this in which the brown graph that slopes downward is the graph
of the top equation (x + y = 4) and the green graph that slopes upward is the graph of the bottom
equation (-x + y = 2):
.

.
You should find that the point (1,3) is where the graphs cross. So x = 1 and y = 3 is the
common solution for both equations. You can plug those values into each equation and verify
that the equations will both balance.
.
Hope this helps you to understand how graphing can be used to solve linear equations.
.

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