# How do you solve #y=4x-9# and #y=x-3# using substitution?

##### 3 Answers

See the entire solution process below:

#### Explanation:

Step 1) Because the first equation is already solve for

Step 2) Substitute

The solution is:

#### Explanation:

Since both equations are

Now solve for

Now substitute

Check by substituting both putting both values into the first equation:

So

Which is the point of intersection:

#### Explanation:

Labelling the equations.

#color(red)(y)=4x-9to(1)#

#color(red)(y)=x-3to(2)# Since both equations have y as the subject we can equate the right sides.

#rArr4x-9=x-3# subtract x from both sides.

#4x-x-9=cancel(x)cancel(-x)-3#

#rArr3x-9=-3# add 9 to both sides.

#3xcancel(-9)cancel(+9)=-3+9#

#rArr3x=6# divide both sides by 3

#(cancel(3) x)/cancel(3)=6/3#

#rArrx=2# Substitute this value into either of the equations

#"Substitute " x=2" in " (2)#

#rArry=2-3=-1#

#color(blue)"As a check"#

#"Substitute " x=2" in "(1)#

#rArry=(4xx2)-9=8-9=-1to" true"#

#rArr(2.-1)" is the point of intersection"#

graph{(y-4x+9)(y-x+3)=0 [-10, 10, -5, 5]}