SOLVE SYSTEMS OF EQUATIONS BY ELIMINATION

Problem 2 :

8x - 6y = -24

-8x + y = 24

Solution :

        8x - 6y = -24 ---> (1)

      -8x + y = 24 ---> (2)

Here coefficients of x are same and they have different signs. So, by adding these two equations, we can eliminate x.

-5y = 0

y = 0

By applying y = 0 in (1) equation, we get

8x - 6(0) = -24

8x - 0 = -24

8x = -24

x = -3

So, the solution is x = -3 and y = 0.

Problem 3 :

-5x + 3y = 2

-5x - 5y = -30

Solution :

 -5x + 3y = 2 ---> (1)

-5x - 5y = -30 ---> (2)

Here coefficients of x are same and they have same signs. So, multiply any one of the equations by -1 and add.

(-5x + 3y)+(5x + 5y) = 2 + 30

8y = 32

y = 4

By applying y = 4 in (1) equation, we get

-5x + 3(4) = 2

-5x + 12 = 2

-5x = 2 - 12

-5x = -10

x = 2

So, the solution is x = 2 and y = 4.

Problem 4 :

7x + y = 6

10x + y = 12

Solution :

        7x + y = 6 ---> (1)

          10x + y = 12 ---> (2)

Here coefficients of x are same and they have same signs. So, multiply any one of the equations by -1 and add.

(7x + y) + (-10x - y) = 6 - 12

7x - 10x + y - y = -6

-3x = -6

x = 2

By applying x = 2 in (1) equation, we get

7(2) + y = 6

14 + y = 6

y = 6 - 14

y = -8

So, the solution is x = 2 and y = -8.

Problem 5 :

12x - 7y = -11

-4x + 4y = 12

Solution :

12x - 7y = -11 ---> (1)

-4x + 4y = 12 ---> (2)

Comparing coefficients of x, multiplying the (2) by 3 we can make it as 12.

12x - 7y + (-12x + 12y) = -11 + 36

5y = 25

y = 5

By applying y = 5 in (1) equation, we get

12x - 7(5) = -11

12x - 35 = -11

12x = -11 + 35

12x = 24

x = 2

So, the solution is x = 2 and y = 5.

Problem 6 :

6x + 2y = 30

9x - 4y = 3

Solution :

6x + 2y = 30 ---> (1)

9x - 4y = 3 ---> (2)

Comparing the coefficients of y, multiplying (1) by 2, we can make the coefficients of y as same.

12x + 4y + 9x - 4y = 60 + 3

21x = 63

x = 3

x = 3

By applying x = 3 in (1) equation, we get

6(3) + 2y = 30

18 + 2y = 30

2y = 30 - 18

2y = 12

y = 6

So, the solution is x = 3 and y = 6.

Problem 7 :

12x - 8y = -12

6x + 4y = -30

Solution :

12x - 8y = -12 ---> (1)

6x + 4y = -30 ---> (2)

Considering the coefficients of y, multiplying (2) by 2, we can make the coefficients same.

12x - 8y + 12x + 8y = -12 - 60

24x = -72

x = -3

By applying x = -3 in (1) equation, we get

12(-3) - 8y = -12

-36 - 8y = -12

-8y = -12 + 36

-8y = 24

y = -3

So, the solution is x = -3 and y = -3.

Problem 8 :

-2x - 7y = -13

3x + 6y = 15

Solution :

-2x - 7y = -13 ---> (1)

3x + 6y = 15 ---> (2)

Considering the coefficients of x, they are not same.

Multiplying (1) by 3 and multiplying (2) by 2, we can make it as same.

-6x - 21y + 6x + 12y = -39 + 30

-9y = -9

y = 1

By applying y = 1 in (1) equation, we get

-2x - 7(1) = -13

-2x - 7 = -13

-2x = -13 + 7

-2x = -6

x = 3

So, the solution is x = 3 and y = 1.