Question

Solve the system of equations graphically. You can use your graphing calculator!

y=−2x−1

3x − y =−7

Answer 1

To solve the system of equations graphically, we will graph both equations and look for the point where the two lines intersect.

First, let's graph the equation y = -2x - 1:
- Start by choosing some x-values and substituting them into the equation to find the corresponding y-values. We'll choose x = -3, -2, 0, 1, 2:
For x = -3: y = -2(-3) - 1 = 5
For x = -2: y = -2(-2) - 1 = 3
For x = 0: y = -2(0) - 1 = -1
For x = 1: y = -2(1) - 1 = -3
For x = 2: y = -2(2) - 1 = -5

Plot these points on the coordinate plane and draw a line that passes through them:

(-3, 5)
|
(-2, 3)
|
(0, -1)
|
(1, -3)
|
(2, -5)
|
-----------------------------------

Next, let's graph the equation 3x - y = -7:
- To graph this equation, solve for y:
y = 3x + 7

Again, choose some x-values and substitute them into the equation to find the corresponding y-values. We'll choose x = -3, -2, 0, 1, 2:
For x = -3: y = 3(-3) + 7 = -2
For x = -2: y = 3(-2) + 7 = 1
For x = 0: y = 3(0) + 7 = 7
For x = 1: y = 3(1) + 7 = 10
For x = 2: y = 3(2) + 7 = 13

Plot these points on the coordinate plane and draw a line that passes through them:

(-3, -2)
|
(-2, 1)
|
(0, 7)
|
(1, 10)
|
(2, 13)
|
-----------------------------------

Now, we can see that the two lines intersect at approximately (-2, 3). This is the solution to the system of equations.