A pair of equations is shown below.
y = -6x - 3
y = -x + 2
Part A: Solve the system of equations using a graph, substitution, or elimination. DO NOT use the same method you used for Question 1. Show or explain everything you did to find the solution.
Part B: Explain what the solution represents.
You may solve by graphing if you did not use that method for Question 1.
Download the provided document, complete your work, save the document, and submit it in the last question of the test.
Module 6 Test Graph.docx
Part A:
To solve the system of equations:
y = -6x - 3
y = -x + 2
I will use the substitution method. I will substitute the second equation into the first equation to solve for x.
Substituting y = -x + 2 into y = -6x - 3:
-x + 2 = -6x - 3
Adding x to both sides:
2 = -5x - 3
Adding 3 to both sides:
5 = -5x
Dividing by -5:
x = -1
Now that I have found the value of x, I will substitute it back into one of the original equations to solve for y. I will use the second equation.
y = -(-1) + 2
y = 1 + 2
y = 3
Therefore, the solution to the system of equations is x = -1 and y = 3.
Part B:
The solution (-1, 3) represents the point where the two equations intersect on the coordinate plane. This is the unique solution to the system of equations, and it is the point where the lines represented by the equations y = -6x - 3 and y = -x + 2 intersect.