To solve the system by graphing, we will graph both equations on the same coordinate plane and find the point(s) where the graphs intersect.
First, let's graph the equation x + y = 2:
To graph this equation, we need to find two points that satisfy the equation.
Let's assign values to x and solve for y:
When x = 0, y = 2; So one point is (0, 2).
When y = 0, x = 2; So another point is (2, 0).
Plotting these points and drawing a straight line passing through them, we get:
| .
| .(2,0)
| .
| .
|_____ .___
(0,2) x
Now, let's graph the equation 2y - x = 10:
To graph this equation, we also need to find two points that satisfy the equation.
Again, let's assign values to x and solve for y:
When x = 0, 2y = 10, so y = 5; So one point is (0, 5).
When y = 0, 2(0) - x = 10, so x = -10; So another point is (-10, 0).
Plotting these points and drawing a straight line passing through them, we get:
|
|
|
|
____|_______
(-10,0) (0,5)
Now, we can see that the two lines intersect at the point (2,0).
Therefore, the solution to the system is x = 2 and y = 0.
2. Solve the system by graphing. State the solution.
x + y =2
2y – x = 10
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