Q:

A pair of equations is shown below: y = 7x βˆ’ 8 y = 5x βˆ’ 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) I need help with part b.

Accepted Solution

A:
Part Ay = 5x - 2 .... start with the second equation7x - 8 = 5x - 2 ... replace y with 7x-8, which is from the first equation7x-8+8 = 5x-2+8 .... add 8 to both sides7x = 5x+67x-5x = 5x+6-5x ... subtract 5x from both sides2x = 62x/2 = 6/2 ..... divide both sides by 2x = 3Use x = 3 to find the value of yy = 7x - 8y = 7*3 - 8y = 21 - 8y = 13We can use the other equation as well to get the same result for yy = 5x - 2y = 5*3 - 2y = 15 - 2y = 13The solution is (x,y) = (3, 13)--------------------------------------------------------------------------Part BThe lines intersect at (3,13)This is If you graphed both equations on the same xy coordinate grid.This point is on both lines at the same time; therefore, the coordinate values of this point satisfy both equations at the same time. As shown belowy = 7x - 813 = 7*3 - 8 .... plug in (x,y) = (3,13)13 = 13 Β .... true equation; this point is on the first linerepeat for the second equationy = 5x - 213 = 5*3 - 213 = 13 ... true equation; this point is on the second lineboth equations are true when (x,y) = (3,13), so this point is on both lines at the same time.