What is the solution of the system? Use elimination. 5x + 7y = 32 and 8x + 6y = 46 (1 point)

Question

I really need help with this. It would help me out a lot. i need the answer as soon as possible.

Answer 1

Elimination method

5x+7y  = 32

Multiple to each side equation  by 8.

40x+56y = 256 --------> (1)

8x+6y =  46

Multiple to each side of above equation by 5.

40x+30y = 230 ---------> (2)

To eliminate the x value subtract equation (2) from (1).

40x+56y = 256

40x+30y = 230

(-)  (-)        (-)

_____________

16y = 26

Divide to each side by 16.

16y/16 = 26/16

⇒ y = 13/8

Substitute the y value in (1).

40x+56*13/8 = 256

40x+91 = 256

Subtract 91 to each side.

40x+91-91 = 256-91

40x = 165

Divide to each side by 40.

40x/40 = 165/40

⇒ x = 33/8

Solution is x = 33/8, y = 13/8.

 

 

Answer 2

Elimination method

The system of equations are 5x + 7y = 32  → (1)

and 8x + 6y = 46 → (2)

Step1:

Multiply two equations by constants to get two equations that contain opposite terms.

5x + 7y = 32 (multiply by 8)  40x + 56y = 256 → (3)

8x + 6y = 46 (multiply by negative -5) - 40x - 30y = - 230 → (4)

To eliminate the x variable add the equations (3) & (4).

  40x + 56y = 256

- 40x - 30y = - 230

_____________________

         26y = 26

            y = 1

Step - 2
Subtitute the value in any one of the equations to solve other variable.

Substitute the y value in equation (1).

5x + 7(1) = 32

5x = 32 - 7

5x = 25

x = 5

Solution x = 5 and y = 1.