Solve the simultaneous equations using substitution method.

Question

I don't understand these, please help.

1. y=x+1, x+y3

2.y=x-2, 3x+y=14

3.y=2x+1, x+3y=14

Answer 1

1)

y= x+1         ...... ( 1 )

x+y = 3       ...... ( 2 )

Substitute y= x+1 is equation (2).

x + x + 1 = 3

2x + 1 = 3

Subtract 1 from each side.

2x + 1 - 1 = 3 - 1

2x = 2

Divide each side by 2

x = 1

Substitute x = 1 in equation ( 1 ).

y= x+1

y = 1+1

   = 2

The solution set is (1,2)

Answer 2

2)

y= x - 2         ...... ( 1 )

3x+y = 14       ...... ( 2 )

Substitute y= x - 2 is equation (2).

3x + x - 2 = 14

4x - 2 = 14

Add 2 to each side.

4x - 2 + 2 = 14 + 2

4x = 16

Divide each side by 4

x = 4

Substitute x = 4 in equation ( 1 ).

y= x - 2

y = 4 - 2

   = 2

The solution set is (4,2)

 

Answer 3

3)

y= 2x + 1         ...... ( 1 )

x+3y = 14       ...... ( 2 )

Substitute y= 2x + 1 is equation (2).

x + 3(2x + 1) = 14

x + 6x +3= 14

7x + 3 = 14

7x = 11

x = 11/7

Substitute x = 11/7 in equation ( 1 ).

y= 2x + 1

y = 2(11/7) + 1

   = 22/7 +1

   = 29/7

The solution set is (11/7,29/7)