Question

A pair of equations is shown below:

y = 3x − 5
y = 6x − 8

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.

Answer 1

A.

y = 3x - 5

y = 6x - 8 We simply subtract the second equation from the first. This eliminates y:

0 = 3x - 6x - 5 - (-8)

0 = -3x - 5 + 8

3x = 3

x = 1

Now substitute for x in first equation:

y = 3(1) - 5

y = -2.

B. x = 1 and y = -2 are the values that satisfy both equations. So the liones will intersect at this point (1, -2).

y = 3x - 5

y = 6x - 8 We simply subtract the second equation from the first. This eliminates y:

0 = 3x - 6x - 5 - (-8)

0 = -3x - 5 + 8

3x = 3

x = 1

Now substitute for x in first equation:

y = 3(1) - 5

y = -2.

B. x = 1 and y = -2 are the values that satisfy both equations. So the liones will intersect at this point (1, -2).

Explanation:

no need for one be sure to parapharse

Answer 2

y = 3x - 5
y = 6x - 8

y = y
3x - 5 = 6x - 8
3x - 6x = -8 + 5
-3x = -3
x = -3/-3
x = 1

y = 3x - 5 ⇒ 3(1) - 5 = 3 - 5 ⇒ y = -2
y = 6x - 8 ⇒ 6(1) - 8 = 6 - 8 ⇒ y = -2

x = 1 ; y = -2 or (1,-2) is the point of intersection.