A pair of equations is shown below:

Question

y = 8x − 9
y = 4x − 1

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 this pair of equations by substitution, we will first solve one of the equations for y and then substitute that expression into the other equation.

Given equations:
y = 8x - 9
y = 4x - 1

Solving the first equation for y:
y = 8x - 9

Now, we substitute this expression of y into the second equation:
8x - 9 = 4x - 1
8x - 4x = 9 - 1
4x = 8
x = 2

Now, we substitute the value of x back into the first equation to find y:
y = 8(2) - 9
y = 16 - 9
y = 7

Therefore, the solution to the pair of equations is:
x = 2, y = 7

Part B:
When the two equations are graphed, the lines representing the two equations will intersect at the point (2,7). This is because the solution we found in Part A (x=2, y=7) is the point of intersection of the two lines. At this point, the values of x and y satisfy both equations simultaneously, meaning that both lines pass through this point.