SOLUTION: Solve the system using the elimination method. Check the solution by substituting into both of the original equations. (If there are infinitely many solutions, enter INFINITELY MAN

Algebra ->  Expressions-with-variables -> SOLUTION: Solve the system using the elimination method. Check the solution by substituting into both of the original equations. (If there are infinitely many solutions, enter INFINITELY MAN      Log On


   

Question 1136760: Solve the system using the elimination method. Check the solution by substituting into both of the original equations. (If there are infinitely many solutions, enter INFINITELY MANY. If there is no solution, enter NO SOLUTION.)
−4x+2y=16
8x−2y=−40
Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
−4x+2y=16
8x−2y=−40
add them
4x=-24
x=-6
substitute into the first
24+2y=16
2y=-8
y=-4
check with second, since the first was used to get the other variable.
-48+8=40
(-6, -4)

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the two equations are:

-4x + 2y = 16
8x -2y = -40

add the two equations together to get 4x = -24

solve for x to get x = -6

replace x with -6 in the first equation to get -4 * -6 + 2y = 16

simplify to get 24 + 2y = 16

subtract 24 from both sides to get 2y = 16 - 24

simplify to get 2y = -8

solve for y to get y = -8 / 2 = -4

you have:

x = -6
y = -4

replace x and y in both original equations by -6 and -4.

the two original equations are:

-4x + 2y = 16
8x - 2y - -40

after replacement, these equations become:

-4 * -6 + 2 * -4 = 16 becomes 24 - 8 = 16 which becomes 16 = 16.

8 * -6 - 2 * -4 = -40 becomes -48 - (-8) = -40 which becomes -48 + 8 = -40 which becomes -40 = -40.

the solutions are confirmed to be good.

the solutions are x = -6 and y = -4