Help on substitution method !?

Question

1. 2x +y = 8
y= 2x-2

2. y=-2x-1
y=4+11

3. 3x-2y=18
y=x-7

4. -2x-3y=11
y=-8x-11

5. y = -7x -19
-8 + 2y = 6

Answer 1

1.

2x +y = 8 ---------------- equation 1
y= 2x-2   ----------------- equation 2

Substitute y = 2x - 2 in equation 1.

2x + 2x - 2 = 8

4x - 2 = 8 add 2 to each side

4x = 10

divide each side by 4

x = 10/4 = 2.5

substitute x = 2.5 in equation 2

y = 2 * 2.5 - 2 = 5 - 2 =3

solution is (2.5, 3)

Answer 2

3.

3x-2y = 18 ------------- equation 1
y = x-7       -------------- equation 2

substitute y = x - 7 in 3x-2y = 18

3x - 2(x-7) = 18

3x - 2x + 14 = 18

x + 14 = 18

subtract 14 from each side

x = 4

substitute x = 4 in y = x-7

y = 3 - 7 = 4

solution is (4, -3)

Answer 3

4. -2x-3y=11
y=-8x-11

substitute y=-8x-11 in -2x - 3y = 11

-2x - 3(-8x - 11) = 11

-2x + 24x + 33 = 11

22x + 33 = 11

subtract 33 from each side

22x = -22

divide each side by 22

x = -1

substitute x = -1 in y=-8x-11

y = -8(-1) - 11

y = 8 -11 = -3

solution is (-1, -3)

Answer 4

2) y = -2x - 1            -> (1)

y = 4 + 11

y = 15                   -> (2)

Substitute y = 15 in equation (1).

15 = -2x - 1

Add1 to each side.

15 +1 = -2x - 1 + 1

16 = -2x

Divide each side by -2.

16/-2 = -2x /-2

Cancel common terms.

16/-2 = x

x = -8.

The solution is (-8, 15).

 

Answer 5

5) y = -7x - 19            -> (1)

-8 + 2y = 6

2y = 6 + 8

2y = 14

y = 7                   -> (2)

Substitute y = 7 in equation (1).

7 = -7x - 19

Add19 to each side.

7 + 19 = -7x - 19 + 19

26 = -7x

Divide each side by -7.

26/-7 = -7x /-7

Cancel common terms.

26/-7 = x

x = -26/7.

The solution is (-26/7, 7).