SOLVING SIMULTANEOUS EQAUTIONS ALGEBRAICALLY

Find the simultaneous solution of the following pairs of equations using an algebraic method:

Problem 1 :

y = x + 1

y = 2x - 3

Solution :

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

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

Substitute y = 2x - 3 in (1)

2x - 3 = x + 1

2x - x = 1 + 3

x = 4

By applying x = 4 in (1), we get

y = 4 + 1

y = 5

So, x = 4 and y = 5.

Problem 2 :

y = x + 4

y = -x + 2

Solution :

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

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

Substitute y = -x + 2 in (1)

-x + 2 = x + 4

-x - x = 4 - 2

-2x = 2

x = -1

By applying x = -1 in (1), we get        

y = -1 + 4

y = 3

So, x = -1 and y = 3.

Problem 3 :

y = x + 2

y = -2x + 5

Solution :

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

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

Substitute y = x + 2 in (2)

x + 2 = -2x + 5

x + 2x = 5 - 2

3x = 3

x = 1

By applying x = 1 in (1), we get         

y = 1 + 2

y = 3

So, x = 1 and y = 3.

Problem 4 :

y = -2x - 4

y = x - 4

Solution :

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

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

Substitute y = x - 4 in (1)

x - 4 = -2x - 4

x + 2x = -4 + 4

x + 2x = 0

3x = 0

x = 0

By applying x = 0 in (1), we get         

y = 0 - 4

y = -4

So, x = 0 and y = -4.

Problem 5 :

y = -x + 4

y = 2x - 8

Solution :

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

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

Substitute y = -x + 4 in (2)

-x + 4 = 2x - 8

-x - 2x = - 8 - 4

- 3x = -12

x = -12/-3

x = 4

By applying x = 4 in (1), we get         

y = -4 + 4

y = 0

So, x = 4 and y = 0.

Problem 6 :

y = 2x + 3

y = 2x - 2

Solution :

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

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

Substitute y = 2x + 3 in (2)

2x + 3 = 2x - 2

2x - 2x = -2 - 3

0 = -5

So, there is no solution.

Problem 7 :

y = 3x + 7

y = -x - 6

Solution :

y = 3x + 7 --->(1)

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

Substitute y = -x - 6 in (1)

-x - 6 = 3x + 7

-x - 3x = 7 + 6

-4x = 13

x = -13/4

By applying x = -13/4 in (2), we get

y = -(-13/4) - 6

y = (13 - 24)/4

y = -11/4

So, x = -13/4 and y = -11/4.

Problem 8 :

y = -2x + 3

y = -2x + 6

Solution :

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

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

Substitute y = -2x + 6 in (1)

-2x + 6 = -2x + 3

-2x + 2x = 3 - 6

0 = -3

So, there is no solution.

Problem 9 :

y = 5 - 3x

y = 10 - 6x

Solution :

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

y = 10 - 6x --->(2)

Substitute y = 5 - 3x in (2)

5 - 3x = 10 - 6x

-3x + 6x = 10 - 5

3x = 5

x = 5/3

By applying x = 5/3 in (1), we get

y = 5 - 3(5/3)

y = 0

So, x = 5/3 and y = 0 is the solution.