How do you solve the system #4x - 3y = 1# and #12x - 9y = 3# by substitution?

1 Answer
May 25, 2015

Dividing both sides of the second equation by #3# we get:

#4x-3y = 1#

which is the same as the first equation.

If we attempt to solve the system by substitution, then we will find that all of the terms in #x# and #y# cancel out, resulting in a true, but otherwise uninformative equation of rational numbers.

For example, if we take the first equation and add #3y# to both sides, then divide both sides by #4# we get:

#x = (3y + 1)/4#

Substitute this in the second equation:

#3 = 12x-9y = 12((3y+1)/4) -9y = 3(3y+1)-9y = 9y+3-9y = 3#

As a result, there are not enough constraints to determine a unique solution, but there are an infinite number of solutions.

These solutions are the points on the line which in slope intercept form is described by the equation:

#y = 4/3x + -1/3#