How do you solve the system using the elimination method for 3x+y=4 and 6x+2y=8?

Jul 8, 2015

Any value of $x$ will satisfy the system of equations with $y = 4 - 3 x$.

Explanation:

Re-arrange the first equation to make $y$ the subject:
$y = 4 - 3 x$

Substitute this for $y$ in the second equation and solve for $x$:
$6 x + 2 y = 6 x + 2 \left(4 - 3 x\right) = 8$

This eliminates $x$ meaning there is no unique solution. Therefore any value of $x$ will satisfy the system of equations as long as $y = 4 - 3 x$.

Jul 8, 2015

You have $\infty$ solutions because the two equations represent two coincident lines!
These two equations are related and represent 2 coincident lines; the second equation is equal to the first multiplied by $2$!
The two equations have $\infty$ solutions (set of $x$ and $y$ values) in common.
You can see this by multiplying the first by $- 2$ and adding to the second:
{-6x-2y=-8
{6x+28=8 adding you get:
$0 = 0$ that it is always true!!!