To solve a system using elimination you need to see which number you will need to cancel out.
ex.
3x + 2y = 9
2x + 6y = 6
in order to eliminate either the x or y value you will have to make a zero pair. in order to make a zero pair you must multiple each equation by a certain number to cross one out.
for this equation I am going to multiply the 3x and 2x so that I can cancel it out to find the y value first. In order to make it a zero pair i need to find a number they can both multiply to thats small. But in order to make a zero pair one must be positive and the other must be negative to equal to 0.
for 2 ill multiply that system by -3 and for 3 ill multiply the system by 2 so the gcf can be 6.
2(3x + 2y = 9)
-3(2x + 6y = 6)
this would change the systems to…
6x + 4y = 18
-6x – 18y = -18
then you need to remove the zero pair (-6x, 6x)
so the equation would now look like:
4y = 18
-18y = -18
then you add each number
so it would now look like
-14y = 0
s0 y would =0
(x, 0)
then to find the x you plug in one of the y values with 0 to either system
3x + 2(0) = 9
3x =9
divide by 3 to put x by itself to = 3
so the answer would be
(3, 0)