Question

solve systems by elimination
Solve x - 2y = 6
3x - 6y = 18

Answer 1

To eliminate the x-variable we multiply the first equation by -3 to get the new system
x - 2y = 6
3x - 6y = 18

Now make a linear combo of the two equations
-3x +6y = -18
3x - 6y = 18
=========
0=0
This expression is called an identity and implies that the lines are coincident (on top of each other) and therefore intersect everywhere along the line. The solution set is often written:\[\left\{ (x,y):x-2y=6 \right\}\]