Question

Solve the systems of equations graphically
y=-2x-1and 3x-y=-7

Answer 1

To solve the system of equations graphically, we need to graph both equations on the same coordinate plane and find the point where they intersect.

For the equation y = -2x - 1, we can choose some arbitrary values for x and calculate the corresponding y values to generate points for the graph. Let's choose x = -2, -1, 0, 1, and 2:

For x = -2:
y = -2(-2) - 1 = 4 - 1 = 3
So one point on the graph is (-2, 3).

For x = -1:
y = -2(-1) - 1 = 2 - 1 = 1
Another point on the graph is (-1, 1).

For x = 0:
y = -2(0) - 1 = -1
Another point on the graph is (0, -1).

For x = 1:
y = -2(1) - 1 = -2 - 1 = -3
Another point on the graph is (1, -3).

For x = 2:
y = -2(2) - 1 = -4 - 1 = -5
Another point on the graph is (2, -5).

Now we can plot these points and draw a line passing through them:

Graph of y = -2x - 1:
_________
| /
| /
| /
| /
| /
| /
| /
|/______

Next, we need to graph the equation 3x - y = -7. To do this, we can solve this equation for y:

3x - y = -7
=> y = 3x + 7

Now we can again choose some arbitrary values for x and calculate the corresponding y values to generate points for the graph. Let's choose x = -2, -1, 0, 1, and 2:

For x = -2:
y = 3(-2) + 7 = -6 + 7 = 1
So one point on the graph is (-2, 1).

For x = -1:
y = 3(-1) + 7 = -3 + 7 = 4
Another point on the graph is (-1, 4).

For x = 0:
y = 3(0) + 7 = 0 + 7 = 7
Another point on the graph is (0, 7).

For x = 1:
y = 3(1) + 7 = 3 + 7 = 10
Another point on the graph is (1, 10).

For x = 2:
y = 3(2) + 7 = 6 + 7 = 13
Another point on the graph is (2, 13).

Now we can plot these points and draw a line passing through them:

Graph of y = 3x + 7:
_______________
| /
| /
| /
| /
| /
| /
| /
|/___________

Finally, we can see that the two lines intersect at approximately (-2, 1). This is the solution to the system of equations graphically.