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

1 Answer
Nov 24, 2016

(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"