How do you solve the system #y= 1.2x - 46# and #y = 0.6x - 0.22# by substitution?

1 Answer
May 19, 2015

Choose one equation to solve for one of the variables in terms of the other variable (your choice). Substitute the solution you get into the other equation.

#y=1.2x-46#
#y=0.6x-0,22#

I choose to solve the first equation for #y# in terms of #x# (because it is already solved for #y# in terms of #x#!)
#y=1.2x-46#

Now replace any #y#'s in the second equation with #1.2x-46#

We get:

#1.2x-46 = 0.6x-0.22#

Solve for #x#.

#1.2x-0.6x = 46-0.22#

#0.6x = 45.78#

#x = 45.78/0.6# (if you have a calculator, you can use it)

#x = 45.78/0.6 = 45.78/(6/10) = 45.78*(10/6) = 457.8/6 = 76.3#

Finally, finish by finding #y#.
We already "solved" the first equation for #y# in terms of #x#
#y=1.2x-46#.

So in the solution, #y = 1.2(76.3)-46 = 45.56#

The solution is:

#x = 76.3# and #y = 45.56#.