Solve the system of equations graphically.

y=−2x−1
3x − y =−7

1 answer

To solve the system of equations graphically, we need to graph both equations on the same coordinate plane and find the point of intersection, which represents the solution to the system.

First, let's graph the equation y = -2x - 1.

To do this, we can start by finding the y-intercept, which is -1. This means that the line intersects the y-axis at the point (0, -1).

Next, we can find the x-intercept by setting y = 0 and solving for x:
0 = -2x - 1
2x = -1
x = -1/2
This gives us the x-intercept at the point (-1/2, 0).

We can now plot these two points on the coordinate plane and draw a straight line through them.

Next, let's graph the equation 3x - y = -7.

We can rewrite this equation in the form y = mx + b:
y = 3x + 7

To graph this equation, we can start by finding the y-intercept, which is 7. This means that the line intersects the y-axis at the point (0, 7).

Next, we can find the x-intercept by setting y = 0 and solving for x:
0 = 3x + 7
-7 = 3x
x = -7/3
This gives us the x-intercept at the point (-7/3, 0).

We can now plot these two points on the coordinate plane and draw a straight line through them.

Now that we have graphed both equations, we can identify the point of intersection.
The point where the two lines intersect is approximately (-2, 3).

Therefore, the solution to the system of equations is x = -2 and y = 3.