QuestionFind the intersection points of the functions: $y=3x+15$ and $y=3-3x$ .

Studdy Solution

STEP 1

Assumptions1. The two functions given are linear functions. . The equations of the functions are $y=3x+15$ and $y=3-3x$ .

STEP 2

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

STEP 3

We can simplify this equation by adding $3x$ to both sides to get all the $x$ terms on one side.
$3x+3x+15 =3-3x+3x$

STEP 4

This simplifies to $6x+15 =3$

STEP 5

Next, subtract $15$ from both sides to isolate the $x$ term.
$x+15-15 =3-15$

STEP 6

This simplifies to $6x = -12$

STEP 7

Finally, divide both sides by $6$ to solve for $x$ .
$x = -12/6$

STEP 8

olving for $x$ gives $x = -2$

STEP 9

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

STEP 10

olving for $y$ gives $y = -6 +15 =9$ So, the point of intersection of the two functions is $(-2,9)$ .

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