Question

Find the point of intersection for the two functions through substitution. Show

Answer 1

Answer:  (-1, 11)

This means x = -1 and y = 11 pair up together.

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Work Shown:

Set the two functions equal to one another. Solve for x.

f(x) = g(x)

-4x+7 = 2x+13

7 = 2x+13+4x ... adding 4x to both sides

7 = 6x+13

7-13 = 6x .... subtract 13 from both sides

-6 = 6x

6x = -6

x = -6/6 ... divide both sides by 6

x = -1

Use this x value in either function

f(x) = -4x+7

f(-1) = -4(-1)+7

f(-1) = 11

or

g(x) = 2x+13

g(-1) = 2(-1)+13

g(-1) = 11

Whichever function you pick, the input x = -1 leads to the output y = 11.

The point of intersection is (x,y) = (-1, 11)

Visual confirmation is shown below.