Algebra one help? linear systems..?

Question

1) y-x = 17
2y+3x=-11

2) 4x-3y = -9
5x-y = 8

3) 3x-3y = -1
12x-2y = 16

Answer 1

(1)

The Equations are

y - x = 17     .......................Equation 1

2y + 3x = -11   .......................Equation 2

Now Equation 1 with 2

2y -2x = 34     .......................Equation 3

Now subtract Equation 3 from Equation 1

2y + 3x  + 11 - ( 2y -2x - 34) = 0

5x + 45 = 0

x = - 9.

Sustitute in Equation (1)

y + 9 = 17

y = 8

Therefore values of x and y are -9 and 8.

Answer 2

(2)

The Equations are

4x - 3y = -9     .......................Equation 1

5x - y = 8   .......................Equation 2

Now Equation 2 with 3

15x -3y = 24     .......................Equation 3

Now subtract Equation 3 from Equation 1

15x -3y - 24 - ( 4x - 3y + 9 ) = 0

11x - 33 = 0

x = 3.

Sustitute in Equation (1)

4*3 - 3y = -9

12 - 3y = -9

3y = 21

y = 7

Therefore values of x and y are 3 and 7.

Answer 3

(3)

The Equations are

3x - 3y = -1     .......................Equation 1

12x - 2y = 16   .......................Equation 2

Now Equation 1 with 4.

12x -12y = -4     .......................Equation 3

Now subtract Equation 3 from Equation 2

12x -12y + 4 - ( 12x - 2y - 16 ) = 0

-10y + 20 = 0

y = 2.

Sustitute in Equation (1)

3x - 3*2 = -1

3x - 6 = -1

3x = 5

x = 5/3

Therefore values of x and y are 5/3 and 2.