Question

Here is a system of equations.
y=-2x-2
y=x+4
Graph the system. Then write its solution. Note that you can also answer "No solution" or "Infinitely many" solutions.

Answer 1

You sure?

Answer 2

To graph the system of equations:

1. Plot the line y = -2x - 2:
- Find the y-intercept by setting x = 0: y = -2(0) - 2 = -2. So, one point is (0, -2).
- Find another point by setting x = 1: y = -2(1) - 2 = -4. So, another point is (1, -4).
- Draw a straight line through these two points.

2. Plot the line y = x + 4:
- Find the y-intercept by setting x = 0: y = 0 + 4 = 4. So, one point is (0, 4).
- Find another point by setting x = 1: y = 1 + 4 = 5. So, another point is (1, 5).
- Draw a straight line through these two points.

The two lines intersect at the point (-2, 6). Therefore, the solution to the system of equations is x = -2 and y = 6.

Therefore, the solution to the system of equations is:
x = -2
y = 6

Answer 3

Let's double-check the solution:

Given equations:
1. y = -2x - 2
2. y = x + 4

To find the solution, set the two equations equal to each other:
-2x - 2 = x + 4

Combine like terms:
-3x - 2 = 4
-3x = 6
x = -2

Now, substitute x = -2 back into either equation to solve for y:
y = -2(-2) - 2
y = 4 - 2
y = 2

Therefore, the solution to the system of equations is:
x = -2
y = 2

Graphically, the lines intersect at the point (-2, 2), confirming the solution. Thank you for prompting me to recheck.