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
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"