Alg II Questions?!?!?

Question

Substitution Method: 

1. Solve y – 3x = 5 by the substitution method.
y + x = 3

Elimination Method:

2. Solve –x – y = 8 using the elimination method.
-2x – y = -1

3. Solve 3x + 2y = 7 using the elimination method.
5x – 2y = 1


Thank you SO much :)

Answer 1

1. The  equations  are   y - 3x = 5  and  y + x = 3

                                    y - 3x - 5  = 0    - >  ( 1)

 y + x  = 3   Therefore  x = 3 - y

 Substitute  the  x  value  in  equation  (1)

 y - 3 ( 3 - y ) - 5  = 0

 y - 9 + 3y - 5 = 0

4y = 14   ->  y = 14 / 4  = 7/ 2

Therefore  x = 3 - 7/2  = - 1/ 2

 The  values  of  x = -1/2 , y = 7/2.

Answer 2

2. The  equations  are  -x -y = 8     ->  (1)

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

Subtract equation (1)  form (2)

  -x - y - 8   = 0

 - 2x - y + 1 = 0

______________

  x  - 9  = 0

Therefore  x = 9

 Substitute  the  x value  in  equation  (1)

 -9 -y = 8

Therefore y = - 17

The values of  x = 9 , y = -17.

Answer 3

3. The  equations  are  3x + 2y  = 7   - > (1)

                                     5x - 2y  = 1   - > (2)

Add  equation  (1) and (2)

 3x + 2y - 7 = 0

 5x - 2y -1   = 0

_______________

8x  - 8  = 0

Therefore  x = 1

Substitute  the  x value  in  equation  (1)

3 (1) + 2y  = 7

2y  =  4

Therefore y = 2

The  values  of x =1 , y = 2 .