Question

A pair of equations is shown below:

y = 8t − 9
y = 4t − 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: t = 2 and y = 7

Part B: Point of intersection is (2,7)

Explanation:

Part A: We are given the pair of equations shown below:

y = 8t - 9 ......... (1)

y = 4t - 1 ............ (2)

We can solve those equations by the elimination method.

We have from [equation (1) - equation (2)], 0 = 4t - 8

⇒ t = 2

Therefore, from equation (2), we get y = 4 ×2 - 1 = 7

Hence, t = 2 and y = 7 is the solution of the given pair of equations.

Part B: As equation (1) and equation (2) are two straight lines, so their solution gives the point of intersection of those two lines on the graph.

Therefore, if we plot t along the X-axis and y along the Y-axis then the point of intersection will be (2,7) point. (Answer)