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QuestionFind the intersection of the functions: y=3x+15y=3x+15 and y=3−3xy=3-3x.

Studdy Solution

STEP 1

Assumptions1. The first function is y=3x+15y=3x+15 . The second function is y=3−3xy=3-3x

STEP 2

To find the point of intersection, we need to set the two functions equal to each other and solve for xx.x+15=−xx +15 = -x

STEP 3

We can start by adding 3x3x to both sides of the equation to get all the xx terms on one side.
3x+3x+15=3−3x+3x3x +3x +15 =3 -3x +3x

STEP 4

implify the equation.
6x+15=36x +15 =3

STEP 5

Next, subtract 1515 from both sides of the equation to isolate the xx term.
x+15−15=3−15x +15 -15 =3 -15

STEP 6

implify the equation.
6x=−126x = -12

STEP 7

Finally, divide both sides of the equation by 66 to solve for xx.
x=−12/6x = -12 /6

STEP 8

implify to find the value of xx.
x=−2x = -2

STEP 9

Now that we have the xx-coordinate of the point of intersection, we can substitute x=−2x = -2 into either of the original equations to find the corresponding yy-coordinate. Let's use the first equation y=3x+15y=3x+15.
y=3(−2)+15y =3(-2) +15

STEP 10

implify the equation to find the value of yy.
y=−6+15y = -6 +15

STEP 11

implify to find the value of yy.
y=9y =9The point of intersection of the two functions is (−,9)(-,9).

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