Question

How do you solve the system `2x + y = 1` and `4x + 2y = −1` by substitution?

Answer 1

Given
`"[1] "2x+y = 1` and
`"[2] "4x+2y = -1`

We would normally rearrange [1] to get an equation for `y`
`"[3] "y = 1-2x`
and then substitute this value into equation [2] to solve for `x`

but
Notice something unusual in this case
The left-side of [2] is exactly 2 times the left-side of [1]
but the right-side of [2] is not 2 times the right-side of [1].

The given equations are a pair of parallel lines with no solution (since they do not intersect).