SYSTEMS OF EQUATIONS WITH SUBSITUTION

Use the method of substitution to solve:

Problem 1 :

x = 1 + 2y

2x + y = 17

Solution :

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

2x + y = 17 --- > (2)

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

2(1 + 2y) + y = 17

2 + 4y + y = 17

2 + 5y = 17

5y = 17 - 2

5y = 15

y = 3

By applying y = 3 in equation (1)

x = 1 + 2(3)

x = 1 + 6

x = 7

So, x = 7 and y = 3.

Problem  2 :

y + 4x = 6

y = 2x + 3

Solution :

y + 4x = 6 --- > (1)

y = 2x + 3 --- > (2)

Substitute y = 2x + 3 in equation (1)

2x + 3 + 4x = 6

6x = 6 - 3

6x = 3

x = 3/6

x = 1/2

By applying x = 1/2 in equation (2)

y = 2(1/2) + 3

y = 3

So, x = 1/2 and y = 3.

Problem 3 :

x = 2y - 6

2x + y = 8

Solution :

x = 2y - 6 --- > (1)

2x + y = 8 --- > (2)

Substitute x = 2y - 6 in equation (2)

2(2y - 6) + y = 8

4y - 12 + y = 8

5y = 8 + 12

5y = 20

y = 4

By applying y = 4 in equation (1)

x = 2(4) - 6

x = 8 - 6

x = 2

So, x = 2 and y = 4.

Problem 4 :

3x - 2y = 5

y = 3 - 4x

Solution :

3x - 2y = 5 --- > (1)

y = 3 - 4x --- > (2)

Substitute y = 3 - 4x in equation (1)

3x - 2(3 - 4x) = 5

3x - 6 + 8x = 5

11x = 5 + 6

11x = 11

x = 1

By applying x = 1 in equation (2)

y = 3 - 4(1)

y = 3 - 4

y = -1

So, x = 1 and y = -1

Problem 5 :

x = 1 - 2y

3x + y = 13

Solution :

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

3x + y = 13 --- > (2)

Substitute x = 1 - 2y in equation (2)

3(1 - 2y) + y = 13

3 - 6y + y = 13

-5y = 13 - 3

-5y = 10

y = -2

By applying y = -2 in equation (1)

x = 1 - 2(-2)

x = 1 + 4

x = 5

So, x = 5 and y = -2.

Problem 6 :

x = 3y + 12

3x - 2y = 8

Solution :

x = 3y + 12 --- > (1)

3x - 2y = 8 --- > (2)

Substitute x = 3y + 12 in equation (2)

3(3y + 12) - 2y = 8

9y + 36 - 2y = 8

7y = 8 - 36

7y = -28

y = -4

By applying y = -4 in equation (1)

x = 3(-4) + 12

x = -12 + 12

x = 0

So, x = 0 and y = -4.

Problem 7 :

y = 3x - 2

2x - 5y = 27

Solution :

y = 3x - 2 --- > (1)

2x - 5y = 27 --- > (2)

Substitute y = 3x - 2 in equation (2)

2x - 5(3x - 2) = 27

2x - 15x + 10 = 27

-13x = 27 - 10

-13x = 17

x = -17/13

By applying x = -17/13 in equation (1)

y = 3(-17/13) - 2

y = (-51/13) - 2

y = -77/13

So, x = -17/13 and y = -77/13.

Problem 8 :

x = 4y - 1

3x + 4y = -1

Solution :

x = 4y - 1 --- > (1)

3x + 4y = -1 --- > (2)

Substitute x = 4y - 1 in equation (2)

3(4y - 1) + 4y = -1

12y - 3 + 4y = -1

16y = -1 + 3

16y = 2

y = 2/16

y = 1/8

By applying y = 1/8 in equation (1)

x = 4(1/8) - 1

x = 1/2 - 1

x = -1/2

So, x = -1/2 and y = 1/8.

Problem 9 :

y = 5x + 7

2x - 3y = 8

Solution :

y = 5x + 7 --- > (1)

2x - 3y = 8 --- > (2)

Substitute y = 5x + 7 in equation (2)

2x - 3(5x + 7) = 8

2x - 15x - 21 = 8

-13x = 8 + 21

-13x = 29

x = -29/13

By applying x = -29/13 in equation (1)

y = 5(-29/13) + 7

y = (-145/13) + 7

y = -54/13

So, x = -29/13 and y = -54/13.