How do you solve by substitution #y = 3x – 4# and #9x – 3y = 14#?

1 Answer
Jun 12, 2015

Answer:

These equations represent parallel lines so there is no solution.

Explanation:

We can attempt a solution as follows:
[1]#color(white)("XXXX")##y = 3x-4#
[2]#color(white)("XXXX")##9x-3y = 14#

Using [1], substitute #(3x-4)# for #y# in [2]
[3]#color(white)("XXXX")##9x-3(3x-4) = 14#
Simplify
[4]#color(white)("XXXX")##4 = 14#
Obviously impossible!

So, what went wrong?
If we take [1] and rearrange it into standard form:
[5]#color(white)("XXXX")##3x-y = 4#
then multiplying by 3
[6]#color(white)("XXXX")##9x-3y =12#

What are we to make of the combination of [2] and [6]?
#color(white)("XXXX")#We have #(9x-3y)# equal to 2 different values!

If we graph these two equations, we would see that they form a pair of parallel lines. (Go ahead; try it. I'll wait).

If two lines are parallel then they do not intersect and there is no point where they are equal.