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

1 Answer
May 26, 2015

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).