How do you solve the system of equations: 6x-8y=2 and 9/2x-6y=3/2?

1 Answer
Aug 5, 2015

Answer:

There is no unique solution to this pair of equations (they are the same equation except for a constant multiple)

Explanation:

[1]#color(white)("XXXX")##6x-8y=2#
[2]#color(white)("XXXX")##9/2x-6y=3/2#

Simplify [2] by multiplying by 2
[3]#color(white)("XXXX")##9x-12y = 3#

Convert [1] and [3] so #y# has equal coefficient values in both
Multiply [1] by 3
[4]#color(white)("XXXX")##18x - 24y = 6#
Multiply [3] by 2
[5]#color(white)("XXXX")##18x-24y = 6#

Note that the equations are identical
#color(white)("XXXX")#(going back through the steps
#color(white)("XXXX")#we can see that [1] multiplied by #3/4# is the same as [2]