-2x-5y=-6 2x-7y=-14

There are a few ways to solve this. We can solve this by graphing, elimination, or substitution.

It looks like elimination will be the easiest way to solve this. To solve two equations by elimination, you basically add these two equations together. Let's do this.

    -2x-5y=-6

+   2x-7y=-14

-----------------------

        -12y = -20

Now we'll solve for y.

 -12y = -20         ---Multiply both sides by a negative

-(-12y)=-(-20)

12y = 20            ---Divide both sides by 12

y = 20/12           ---reduce the fraction by dividing he top and bottom by 4

y = 5/3

 

Now we put y in one of the original equations to solve for x. Let's pick the first equation.

-2x-5y=-6 

-2x-5(5/3)=-6 

-2x -25/3= -6                ---Multiply everything by a negative

2x +25/3 = 6               ---subtract 25/3 from both sides

2x = 6 - 25/3

2x = 6/1 - 25/3

2x = 18/3 - 25/3

2x = -7/3                      ---Divide btoh sides by 2

x = -7/3 ÷ 2

x = -7/3*1/2

x= -7/6

 

Our solution is that x = -7/6, and y = 5/3.