Me plz

find the soultion to the system of linear equation using the elimination method.

1. 2x – 3y = -2
2x + y = 14

2. x = -6y - 3
8x + 8y = -24

3. 5x + 5y = 20
-3x + 5y =4

(1) x = 5 , y = 4

(2) x = -3 and y = 0

(3) x = 2 and y = 2

Step-by-step explanation:

(1) 2x - 3y = -2   equation 1

   2x + y = 14 equation 2

solving the system of linear equation by elimination method. We need to decide the variable to eliminate first , in this case , since the coefficient of x are the same  and they have the same signs (+), we can eliminate the variable x first by subtracting equation 1 from equation 2, so we have

2x - 2x + y - (-3y ) = 14 - ( - 2)

4y = 16

divide through by 4

y = 4

substitute y = 4 into equation 1 , we have

2x - 3 (4) = -2

2x - 12 = -2

2x = -2 + 12

2x = 10

x = 5

Therefore :

x = 5 and y = 4

(2) x = -6y - 3 equation 1

    8x + 8y = -24 equation 2

Solving the system of linear equation by substitution method , substitute x = -6y - 3 into equation 2 , equation 2 becomes

8(-6y - 3 ) + 8y = -24

expanding , we have

-48y - 24 + 8y = -24

-40y - 24 = -24

Add 24 to both sides , we have

- 40y = -24 + 24

-40y = 0

divide through by -40

y = 0/-40

y = 0

substitute y = 0 into equation 1 , equation 1 then becomes

x = -6(0) - 3

x = -3

Therefore : x = -3 and y = 0

(3)  5x + 5y = 20 equation 1

    -3x + 5y = 4   equation 2

solving the system of linear equation by elimination method , we have to decide the variable to eliminate first , since the coefficient of y are the same and are both positive, we will eliminate y by subtracting equation 2 from equation 1 , we have

5x - (-3x) + 5y - 5y = 20 - 4

5x + 3x + 0 = 16

8x = 16

x = 2

substitute x = 2 into equation 1 , equation becomes

5(2) + 5y = 20

10 + 5y = 20

5y = 20 - 10

5y = 10

y = 2

Therefore : x = 2 and y = 2

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