Question

3.

(08.03/08.05 MC)

A pair of equations is shown below:

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

y = 8x − 9 (1)

y = 4x − 1 (2)

If using elimination,

Multiply (2) by -2 and add to (1)

Solve for y

Then using any equation, solve for x

y = 8x - 9

-2y = -8x + 2

Part B

-y = -7

y = 7

7 = 8x - 9

16 = 8x

x = 2

The point of intersection of two lines is also the solution to the system of equations of those lines

Hence, these two lines intersect at (2,7)

Answer 2

see below

Explanation:

y = 8x − 9

y = 4x − 1

Since both equations are equal to y, we can set them equal to each other

8x-9 = 4x-1

Subtract 4x from each side

8x-4x-9 = 4x-4x-1

4x-9 = -1

Add 9 to each side

4x-9+9 = -1+9

4x = 8

Divide each side by 4

4x/4 = 8/4

x=2

Now find y

y = 4x-1

y = 4(2)-1

y = 8-1

y = 7

(2,7)

The point of intersection when the 2 lines are graphed is (2,7)