SOLUTION: Solve one using elimination and one using substitution; 1)4x-y=10 -3x+y=-6 2)5x-3y=16 2x+7y=-10

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Question 558688: Solve one using elimination and one using substitution;
1)4x-y=10
-3x+y=-6
2)5x-3y=16
2x+7y=-10
Found 2 solutions by mananth, solver91311:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
4 x -1 y = 10 .............1
-3 x + 1 y = -6 .............2

Add the two equations
x = 4
/ 1
x = 4
plug value of x in (1)
4 x + -1 y = 10
16 + -1 y = 10
-1 y = 10 -16
-1 y = -6
y = 6
(4,6)
-
5 x -3 y = 16 .............1
7 y = -10 -2 x ---------2
/ 7 =
y = -1.43 -0.29 x
Substitute y in (1)
5 x -3 ( -1.43 -0.29 x ) =
5 x + 4.29 + 0.86 x = 16
5 x + 0.86 x = 16 -4.29
5.86 x = 11.71
/ 5.86
x= 2
Plug the value of x in (1)
5 x -3 y = 16
5 * 2 -3 y = 16
10 -3 y = 16
-3 y = 6
/ -3

(2,-3)

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Notice that the coefficient on in the first equation is the additive inverse of the coefficient on in the second equation. Just add the equations:

Notice that the variable (in this case) is eliminated, hence the name Elimination Method.

Substitute the calculated value back into either given equation:

The solution set is

John

My calculator said it, I believe it, that settles it