Question

3 (x – 1) + y – 2 = 0 ; 5x + 2y = 9 simultaneous equation​

Answer 1

Answer :-

The value of x = 1 and y = 2.

Equations given :-

i.) 3(x - 1) + y - 2 = 0

ii.) 5x + 2y = 9

Solution :-

Solving this through substitution method.

• Solving first equation,

=> 3(x - 1) + y - 2 = 0

=> 3x - 3 + y - 2 = 0

=> 3x + y - 5 = 0

=> y = -3x + 5

Taking this equation as iii.)

• Now solving second equation,

=> 5x + 2y = 9

Substituting the value of y from eq. iii.)

=> 5x + 2(-3x + 5) = 9

=> 5x - 6x + 10 = 9

=> -x + 10 = 9

=> -x = 9 - 10

=> -x = -1

Minus (-) sign gets cancelled both sides.

=> x = 1

Taking this equation as iv.)

• Now substituting the value of x from eq. vi. in eq. iii.,

Eq. iii.)

=> y = -3x + 5

=> y = -3 × 1 + 5

=> y = -3 + 5

=> y = 2

Therefore, the value of x is 1 and y is 2.

Answer 2

Given :

• 3(x - 1) + y - 2 = 0

• 5x + 2y = 9

To find :

• The value of x and y

Solution :

→ 3(x - 1) + y - 2 = 0

→ 3x - 3 + y - 2 = 0

→ 3x + y - 5 = 0

→ 3x + y = 5 ------(1)

→ 5x + 2y = 9 -----(2)

Taking equation (1) and (2) :-

Multiplying the first equation by 2 :

→ (3x + y = 5) × 2

→ 6x + 2y = 10 ------(3)

Multiplying the second equation by 1 :

→ (5x + 2y = 9) × 1

→ 5x + 2y = 9 ------(4)

Solving (3) and (4) :-

Subtracting (3) from (4) -

→ 6x + 2y = 10

→ 5x + 2y = 9

⠀(-)⠀(-)⠀⠀⠀(-)

____________

→ x⠀= 1

____________

→ x = 1

Substitute the value of x in 1st equation :-

→ 3x + y = 5

→ 3(1) + y = 5

→ 3 + y = 5

→ y = 5 - 3

→ y = 2

Therefore, the value of x = 1 and y = 2