How to solve using the substitution method?

Question

1. Y= 4x -9 and y=x-3
2. Y=-5 and 5x+4y=-20
3.4x+2y =10 and x-y=13
4.6x+8y= -22 and y=-5
5. 7x+2y=-19 and -x-2y=21
6. -7x +4y= 4x -4y=0
7. -7x+2y=18 and 6x+6y=0
8.3x-5y =17 and y=-7
9. 4x-y=20 and -x-6y =4

Answer 1

Substitution method

1)The system of equations are y = 4x - 9 and y = x - 3.

Find the value of x  by substituting x - 3 for y in the First equation.

x - 3 = 4x - 9

- 3x = - 6

x = 2

Substitute the x value in second equation.

y = 2 - 3

y = -1

Solution x = 2, y = -1.

2)The system of equations are y = - 5 and 5x + 4y = - 20

Find the value of x  by substituting - 5 for y in the second equation.

5x + 4(- 5) = - 20

5x - 20 = - 20

5x = 0

x = 0

Substitute the x value in second equation.

5(0) + 4y = - 20

4y = -20

y = -5

Solution x = 0, y = - 5.

3)The system of equations are 4x + 2y = 10 and x - y = 13

From second equation y = x - 13

Find the value of x  by substituting x - 13 for y in the first equation.

4x + 2(x - 13) = 10

4x + 2x - 26 = 10

6x = 36

x = 6

Substitute the x value in second equation.

x - y = 13

6 - y = 13

y = - 7

Solution x = 6, y = - 7.

4)The system of equations are 6x + 8y = - 22 and y = - 5

Find the value of x  by substituting - 5 for y in the first equation.

6x + 8(-5) = -22

6x - 40 = -22

6x = 18

x = 3

Substitute the x value in first equation.

6(3) + 8y = - 22

18 + 8y = - 22

8y = - 40

y = - 5

Solution x = 3, y = - 5.

5)The system of equations are 7x + 2y = - 19 and - x - 2y = 21

From second equation x = - 2y - 21

Find the value of y  by substituting - 2y - 21 for x in the first equation.

7( - 2y - 21) + 2y = -19

- 14y - 147 + 2y = -19

- 12y = 128

y = -128/12

y = -32/3

Substitute the y value in second equation.

- x - 2( - 32/3) = 21

- x + 64/3 = 21

x = 64/3 - 21

x = (64-63)/3

x = 1/3

Solution x = 1/3, y = - 32/3.

 

Answer 2

6)The system of equations are - 7x + 4y = 4 and x - 4y = 0

From second equation x = 4y

Find the value of y  by substituting 4y  for x in the first equation.

- 7(4y) + 4y = 4

- 28y + 4y = 4

- 24y = 4

y = -1/6

Substitute the y value in second equation.

x - 4(-1/6) = 0

x + 4/6 = 0

x = - 2/3

Solution x = - 2/3, y = -1/6.

7)The system of equations are - 7x + 2y = 18 and 6x + 6y = 0

From second equation x = - y

Find the value of y  by substituting - y  for x in the first equation.

- 7(- y) + 2y = 18

7y + 2y = 18

9y = 18

y = 2

Substitute the y value in second equation.

6x + 6(2) = 0

6x = - 12

x = - 2

Solution x = - 2, y = 2.

8) The system of equations are 3x - 5y = 17 and y = - 7

Find the value of x  by substituting - 7 for y in the first equation.

3x - 5(- 7) = 17

3x + 35 = 17

3x = - 18

x = - 6

Substitute the x value in first equation.

3(- 6) - 5y = 17

-18 - 5y = 17

5y = - 35

y = - 7

Solution x = - 6, y = - 7.

9)The system of equations are 4x - y = 20 and - x - 6y = 4

From second equation x = - 6y - 4

Find the value of y  by substituting - 6y - 4  for x in the first equation.

4(- 6y - 4) - y = 20

- 24y  - 16 - y = 20

- 25y - 16 = 20

25y = - 36

y = - 36/25

Substitute the y value in second equation.

- x - 6y = 4

- x - 6(-36/25) = 4

- x + 216/25 = 4

x = 216/25 - 4

x = (216 - 100)/25

x = 116/25

Solution x = 116/25, y = -36/25.