Use the elimination method

1) 3x+y=-1 5x-y=9

2) 4x+6y=24 4x-y=10

3) 2x-y=-3 x+3y=16

4) 2x+3y=7 3x+4y=10

1) 3x+y=-1 5x-y=9

First of all we have add both equation but to be sure that the value we want to eliminate are both in a way that would make it possible t be deleted.

3x+y=-1

5x-y = 9

8x = 8

x = 1

In this case we are able to eliminate y becuase if we add + y-y we get that our answer is 0. and 3x + 5x would be 8x and - 1+9 would be equal to 8 and to find x we needed to divided giving us that the answer for x is 1 becuase 8/8 is 1.

Then to find y we substitude the value of x in any of the formulas.

3 (1) + y = - 1

3+y = - 1

y = - 1-3

y=-4

When we have our y value we can determine if it is correct by replace the values.

5 (1) - - 4 = 9

5+4 = 9

9=9

Up until now we are fine. So we do the same with the other equation.

3 (1) + - 4=-1

3+-4=-1

-1=-1

So by this we can now detemine that.

x = 1

y = - 4

2) 4x+6y=24 4x-y=10

4x + 6y = 24

4x-y=10 (*-1)

4x+6y=24

-4x+y=-10

7y = 14

y = 14/7

y = 2

In this case we are not able to delete any of the variables so we multiplied by - 1 to be able to eliminate x.

Then to find x we substitute the value of y in any of the formulas.

4x-2=10

4x = 10+2

x = 12/4

x = 3

So we now know our variables so we substituted them to see if they are correct.

4 (3) + 6 (2) = 24

12+12=24

24=24

We do the same with the other equation.

4 (3) - 2=10

12-2 = 10

10 = 10

So we can assume that.

x = 3

y = 2

3) 2x-y=-3 x+3y=16

(3*) 2x - y = - 3

x + 3y = 16

6x - 3y = - 9

x+3y = 16

7x = 7

x = 1

In this case we are not able to delete any of the variables so we multiplied by 3 to be able to eliminate y.

Then to find y we substitute the value of x in any of the formulas.

1 + 3y = 16

3y = 16-1

y = 15/3

y = 5

So we now know our variables so we substituted them to see if they are correct.

2 (1) - 5 = - 3

2-5 = - 3

-3 = - 3

We do the same with the other equation.

1+3 (5) = 16

1+15=16

16=16

So we now are sure that

x = 1

y = 5

4) 2x+3y=7 3x+4y=10

2x+3y = 7 ( * - 4)

3x+4y = 10 ( * 3)

-8x - 12y = - 28

9x + 12y = 30

x = 2

In this case we are not able to delete any of the variables so we multiplied one of teh quations by - 4 to be able to subtract in our sum and the other by 3 to have the same number on y to be able to eliminate y.

Then to find y we substitute the value of x in any of the formulas.

2 (2) + 3y = 7

4+3y=7

3y = 7-4

y = 3/3

y = 1

So we now know our variables so we substituted them to see if they are correct.

3 (2) + 4 (1) = 10

6+4=10

10=10

We do the same for the other

2 (2) + 3 (1) = 7

4+3 = 7

7=7

So with that we can say that.

x = 2

y = 1