Solve the system by graphing. Check your solution
y=x
y=-x+4
To solve the system by graphing, we first need to graph the two equations:
1) y = x
2) y = -x + 4
Here is the graph of both equations:
Graph:
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y | /
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x
From the graph, we can see that the lines intersect at the point (2, 2). Therefore, the solution to the system is x = 2 and y = 2.
Now let's check this solution by substituting it back into the original equations:
1) y = x
2 = 2 --> the solution satisfies the equation y = x.
2) y = -x + 4
2 = -(2) + 4 --> -4 + 4 = 2 --> 0 = 2
The solution satisfies the equation y = -x + 4.
Therefore, the solution (x = 2, y = 2) is correct and satisfies both equations.