Question

What is the solution of the system? Use elimination. -12x-y=6 17x+y=4

Answer 1

Elimination means that you add or subtract multiples of the equations so that one of the variables cancel out.
Here, noting that -y appears in the first equation, and +y appears in the second.
So by simply adding the first equation to the second, we will have eliminated y, resulting in an equation containing x only.
Solve this last equation for x, and back substitute in the first equation to find y.
Finally, using the calculated values of x and y, substitute back into EACH of the equations to make sure that you have the correct answer.

Example:
4x+3y=7
2x-3y=-1
Here again, we have +3y and -3y, we simply add to eliminate y.
(4x+2x)+0y=7-1
6x=6
x=1
Put x=1 into the first equation to solve for y
4(1)+3y=7
3y=7-4
3y=3
y=1

Now put x=1, y=1 into the first equation:
4(1)+3(1)=4+3=7 ....checks
2(1)-3(1)=2-3=-1 .... checks
So (x,y)=(1,1)

Answer 2

Thank you