# How do you solve the system of equations: x = 3 - 2y ; 2x + 4y = 6?

Aug 15, 2015

You get: $\infty$ number of solutions!
Take the first equation and substitute into the second for $x$:
$2 \left(\textcolor{red}{3 - 2 y}\right) + 4 y = 6$
$6 \cancel{- 4 y} \cancel{+ 4 y} = 6$
$6 = 6$!!!
In reality the second equation is equal to the first multiplied by $2$!!!
You have the equations of 2 coincident lines, or, two lines one superimposed over the other, so, your system will have $\infty$ solutions (i.e., $\infty$ points in common).