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

Answer:

#(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"#