Solve the system by graphing. Check your solution.
y=-x-7
y=x-1
To solve the system by graphing, we will plot the equations on a coordinate plane and find the point where they intersect.
First, let's graph the equation y = -x - 7:
y-intercept: When x = 0, y = -0 - 7 = -7. So the y-intercept is (0, -7).
x-intercept: When y = 0, -x - 7 = 0. Solving for x, we get x = -7. So the x-intercept is (-7, 0).
Plotting these two points and drawing a line passing through them, we get:
```
|
0 | x x
|
---------------------------------
```
Next, let's graph the equation y = x - 1:
y-intercept: When x = 0, y = 0 - (-1) = 1. So the y-intercept is (0, 1).
x-intercept: When y = 0, x - 1 = 0. Solving for x, we get x = 1. So the x-intercept is (1, 0).
Plotting these two points and drawing a line passing through them, we get:
```
|
1 | x
|
|
0 | x x
|
---------------------------------
```
Now, we can see that the two lines intersect at the point (3, -4). Therefore, the solution to the system of equations is x = 3 and y = -4.
To check the solution, we substitute x = 3 and y = -4 into the given equations:
For the equation y = -x - 7:
-4 = -(3) - 7
-4 = -3 - 7
-4 = -10 (true)
For the equation y = x - 1:
-4 = 3 - 1
-4 = 2 (false)
Therefore, the solution x = 3 and y = -4 is only consistent with the first equation, and not the second equation.
just tell me were to graph
Sure!
To graph the equation y = -x - 7:
1. Plot the point (0, -7) on the y-axis.
2. Use the slope (-1), which means for every 1 unit you move to the right, you move 1 unit down. And for every 1 unit you move to the left, you move 1 unit up. Connect the point (0, -7) to another point using this slope. Repeat this process until you have enough points to draw a line.
To graph the equation y = x - 1:
1. Plot the point (0, -1) on the y-axis.
2. Use the slope (1), which means for every 1 unit you move to the right, you move 1 unit up. And for every 1 unit you move to the left, you move 1 unit down. Connect the point (0, -1) to another point using this slope. Repeat this process until you have enough points to draw a line.
Once both lines are graphed, find the point where they intersect. The coordinates of this point will be the solution to the system.