Question

Graph the system of equations below to find the solution.
x+y=8
x-y=-2

Answer 1

To graph the system of equations, we can rearrange both equations to solve for y in terms of x:

1) x + y = 8
y = 8 - x

2) x - y = -2
y = x + 2

Now we can plot the two equations on a coordinate plane:

For the first equation, we start at the y-intercept, which is 8. From there, we can use the slope, which is -1, to find another point. Since the slope is -1, we can go down 1 and to the right 1 from the y-intercept to find a second point. Connecting these two points gives us the graph of the first equation.

For the second equation, we start at the y-intercept, which is 2. From there, we can use the slope, which is 1, to find another point. Since the slope is 1, we can go up 1 and to the right 1 from the y-intercept to find a second point. Connecting these two points gives us the graph of the second equation.

The solution to the system of equations is the point where the two graphs intersect. By analyzing the graph, we can see that the solution is (3, 5).

Here is the graph of the system of equations:
(https://www.desmos.com/calculator/s2eve0cj8f)