Solve by Elimination method .

Question

4x-2y=26

3x+4y=-8

 

Determine the solution of the system. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A)___ (type an ordered pair.)

b). There are infinitely many solutions.

c) There are no soultion.

Answer 1

To solve by elimination, you want to get the coefficient of either x or y to be the same in both equations.  Then you can add or subtract the equations to eliminate whichever variable that is.

 

In this case, you see that there's -2y in the first equation and 4y in the second.  So if you multiply the first equation by 2, the coefficient of y in that equation will be -4.  Then you can add the two equations to eliminate y:

 

4x - 2y = 26

3x + 4y = -8

 

Multiply the first equation by 2:

8x - 4y = 52

3x + 4y = -8

 

Add the equations together:'

8x + 3x + -4y + 4y = 52 + -8

11x = 44

 

Solve for x:

x = 4

 

Now put 4 in for x in one of the equations so you can solve for y:

3x + 4y = -8

3*4 + 4y = -8

12 + 4y = -8

4y = -20

y = -5

 

So the answer is A and the ordered pair is (4, -5)