SOLUTION: Please help me out with this questions 6x +7y = 12 - 4x + y = 26 what is the solution of the system? 6m + n = 46 m – 6n =20 what is the solution of the system? 9x

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Question 141306: Please help me out with this questions
6x +7y = 12
- 4x + y = 26
what is the solution of the system?

6m + n = 46
m – 6n =20
what is the solution of the system?

9x -3y = -114
2x + 24 =y
what is the solution of the system?

9x + 8y = 2
-9x + y =61
what is the solution of the system?

If the perimeter of a rectangle is 52 m. the length is 2 m more than twice the width. Find the dimensions. What is the length
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Eq. 1: 6x+%2B7y+=+12
Eq. 2: -+4x+%2B+y+=+26

Multiply equation 2 by -7:
Eq. 1: 6x+%2B+7y+=+12
Eq. 2: 28x+-7y+=+-182

Now the coefficients on the y terms are additive inverses.

Add the equations, term by term:
Sum Eq.: 34x+%2B0y=-170

Solve for x:
34x=-170
x=-5

Substitute this value for x in either equation:
Eq. 1: 6%28-5%29+%2B+7y+=+12

Solve for y:
-30+%2B+7y+=+12
7y+=+12+%2B+30
7y=42
y=6

The solution set is the ordered pair (-5,6).

Solve the other systems by the same method. You may have to find multipliers for both equations in some situations so that you end up with additive inverse coefficients on one of the variables.

The last problem is just realizing that the perimeter is 2L + 2W = 52, and that you are given that L = 2W + 2. Substitute this expression for L in the perimeter equation and solve for W.