Question

A pair of equations is shown below:

y = 7x − 8
y = 5x − 2

Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points)

Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)

Answer 1

Part A: To solve the pair of equations by substitution, we will solve one of the equations for one of the variables and substitute it into the other equation. For example, we can solve the second equation for y:

y = 5x - 2

Then, we can substitute this expression for y into the first equation:

7x - 8 = 5x - 2

Next, we will isolate x by subtracting 5x from both sides:

2x - 8 = -2

Then, we will add 8 to both sides:

2x = 6

Finally, we will divide both sides by 2:

x = 3

Now that we have solved for x, we can substitute this value back into one of the original equations to solve for y. Let's use the second equation:

y = 5x - 2

y = 5(3) - 2

y = 13

Therefore, the solution to the pair of equations is x = 3 and y = 13.

Part B: If the two equations are graphed, the lines representing the two equations will intersect at the point (3, 13). This is because the solution to the pair of equations is the point where the two lines intersect. We found in Part A that x = 3 and y = 13, so the point (3, 13) is the solution to the pair of equations.