Question

What are the coordinates of the one point shared in common between the two linear functions given: `y=2x-2, 3y=-x+15`?

Answer 1

`(3,4)`

Explanation:

To find a common point, solve the equations `color(blue)"simultaneously"`

We are given y = 2x - 2. Substitute this value for y into the other equation and solve for x.

`rArr3(2x-2)=-x+15`

distribute the bracket, collect terms in x on the left side and numeric values on the right side.

`rArr6x-6=-x+15`

add x to both sides.

`6x+x-6=cancel(-x)cancel(+x)+15`

`rArr7x-6=15`

add 6 to both sides.

`7xcancel(-6)cancel(+6)=15+6`

`rArr7x=21`

To solve for x, divide both sides by 7

`(cancel(7) x)/cancel(7)=21/7rArrx=3`

To find the corresponding value of y, substitute x = 3 into
y = 2x - 2

`rArry=(2xx3)-2=6-2=4`

`rArr(3,4)" is a common point"`

Check :

Using x = 3 then y should be 4 for both equations.

`rArry=2x-2=(2xx3)-2=4larr" True"`

`rArr3y=-x+15=-3+15=12rArry=4larr" True"`

`"Thus" (3,4)" is a common point to both equations"`