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

Studdy Solution

STEP 1

Assumptions1. The first function is $y=3x+15$ . The second function is $y=3-3x$
3. We are looking for the point(s) of intersection, which are the values of $x$ and $y$ where the two functions are equal.

STEP 2

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

STEP 3

To isolate $x$ , we can start by combining like terms. Add $3x$ to both sides of the equation.
$3x +3x +15 =3 -3x +3x$

STEP 4

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

STEP 5

Next, subtract15 from both sides to isolate the term with $x$ .
$x +15 -15 =3 -15$

STEP 6

implify the equation.
$6x = -12$

STEP 7

Finally, divide both sides by6 to solve for $x$ .
$x = -12 /6$

STEP 8

implify to find the value of $x$ .
$x = -2$

STEP 9

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

STEP 10

implify to find the value of $y$ .
$y = -6 +15 =9$ The point of intersection of the two functions is $(-2,9)$ .

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

Studdy Solution

STEP 1

Assumptions1. The first function is $y=3x+15$ . The second function is $y=3-3x$
3. We are looking for the point(s) of intersection, which are the values of $x$ and $y$ where the two functions are equal.

STEP 2

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

STEP 3

To isolate $x$ , we can start by combining like terms. Add $3x$ to both sides of the equation.
$3x +3x +15 =3 -3x +3x$

STEP 4

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

STEP 5

Next, subtract15 from both sides to isolate the term with $x$ .
$x +15 -15 =3 -15$

STEP 6

implify the equation.
$6x = -12$

STEP 7

Finally, divide both sides by6 to solve for $x$ .
$x = -12 /6$

STEP 8

implify to find the value of $x$ .
$x = -2$

STEP 9

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

STEP 10

implify to find the value of $y$ .
$y = -6 +15 =9$ The point of intersection of the two functions is $(-2,9)$ .

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

Studdy Solution

STEP 1

Assumptions1. The first function is y=3x+15y=3x+15y=3x+15 . The second function is y=3−3xy=3-3xy=3−3x3. We are looking for the point(s) of intersection, which are the values of xxx and yyy where the two functions are equal.

STEP 2

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

STEP 3

To isolate xxx, we can start by combining like terms. Add 3x3x3x to both sides of the equation.3x+3x+15=3−3x+3x3x +3x +15 =3 -3x +3x3x+3x+15=3−3x+3x

STEP 4

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

STEP 5

Next, subtract15 from both sides to isolate the term with xxx.x+15−15=3−15x +15 -15 =3 -15x+15−15=3−15

STEP 6

implify the equation.6x=−126x = -126x=−12

STEP 7

Finally, divide both sides by6 to solve for xxx.x=−12/6x = -12 /6x=−12/6

STEP 8

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

STEP 9

Now that we have the xxx value, we can substitute it into either of the original equations to solve for yyy. Let's substitute x=−2x = -2x=−2 into the first equation y=3x+15y =3x +15y=3x+15.y=3(−2)+15y =3(-2) +15y=3(−2)+15

STEP 10

implify to find the value of yyy.y=−6+15=9y = -6 +15 =9y=−6+15=9The point of intersection of the two functions is (−2,9)(-2,9)(−2,9).

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

Assumptions1. The first function is $y=3x+15$ . The second function is $y=3-3x$
3. We are looking for the point(s) of intersection, which are the values of $x$ and $y$ where the two functions are equal.

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

To isolate $x$ , we can start by combining like terms. Add $3x$ to both sides of the equation.
$3x +3x +15 =3 -3x +3x$

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

Next, subtract15 from both sides to isolate the term with $x$ .
$x +15 -15 =3 -15$

implify the equation.
$6x = -12$

Finally, divide both sides by6 to solve for $x$ .
$x = -12 /6$

implify to find the value of $x$ .
$x = -2$

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

implify to find the value of $y$ .
$y = -6 +15 =9$ The point of intersection of the two functions is $(-2,9)$ .