How do I solve these equations using substitution?

Question

-7x+2y=18 and 6x+6y=0 


7x+2y= -19 and -x+2y=21 


3x-5y=17 and y= -7 


-7x+4y=24 and 4x-4y=0

 

 

Answer 1

1)

The equations are

-7x+2y = 18    --------- (1)

6x+6y = 0

6y = -6x

y = - x             --------- (2)

Substitute y = - x in (1).

-7x+2y = 18 ⇒ -7x+2(-x) = 18

-7x - 2x = 18

-9x = 18

9x = -18

x = - 18 / 9

x = - 2

Substitute x = - 2 in (2).

y = - x

y = - (-2)

y = 2

Solution :

x = - 2 and y = 2

Answer 2

2)

The equations are

7x + 2y = -19          --------- (1)

- x + 2y = 21

2y = 21 + x             --------- (2)

Substitute 2y = 21 + x  in equation (1).

7x + 2y = -19 ⇒ 7x + (21 + x) = -19

7x + 21 + x = -19

8x = - 19 - 21

8x = - 40

x = - 40 / 8

x = - 5

Substitute x = - 5 in equation (2).

2y = 21 + (- 5)  

2y = 21 - 5

2y = 16

y = 16/2

y = 8

Solution :

x = - 5 and y = 8.

Answer 3

3)

The equations are

3x-5y=17    --------- (1)

y = - 7             --------- (2)

Substitute y = - 7 in (1).

3x - 5y = 17 ⇒ 3x - 5(-7) = 17

3x + 35 = 17

3x = 17 - 35

3x = - 18

x = - 18 / 3

x = - 6

Solution :

x = - 6 and y = -7.

 

Answer 4

4)

The equations are

-7x + 4y = 24    --------- (1)

4x-4y=0

4y = 4x

y =  x             --------- (2)

Substitute y =  x in (1).

-7x + 4y = 24  ⇒ -7x + 4x = 24

- 3x = 24

3x = - 24

x = - 24 / 3

x = - 8

Substitute x = - 8 in (2).

y = x

y = - 8

Solution :

x = - 8 and y = - 8