Solve the system by graphing. Check your solution

Question

y=x
y=-x+4

Answer 1

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:

| /
| /
y | /
| /
| /
--------------------------------
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.