Question

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

Answer 1

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]