Question

The number of solutions of the pair of linear equations 3x-5y=-1 and 6x-y=7 is​

Answer 1

Step-by-step explanation:

Hope helpful for you Mark me as brainlist please

Answer 2

SOLUTION

TO DETERMINE

The number of solutions of the pair of linear equations 3x - 5y = - 1 and 6x - y = 7

CONCEPT TO BE IMPLEMENTED

For the given two linear equations

$\displaystyle \sf{ a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0}$

Consistent :

One of the Below two condition is satisfied

1. Unique solution :

$\displaystyle \sf{ \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2} }$

2. Infinite number of solutions :

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} = \: \frac{c_1}{c_2}}$

Inconsistent :

NO solution

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \: \frac{c_1}{c_2}}$

EVALUATION

Here the given system of equations are

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

6x - y = 7 - - - - - - - - (2)

Comparing with the equation

a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 we get

a₁ = 3 , b₁ = - 5 , c₁ = 1 and a₂ = 6 , b₂ = - 1 , c₂ = - 7

Now

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{3}{6} = \frac{1}{2} }$

$\displaystyle \sf{ \frac{b_1}{b_2} = \frac{ - 5}{ - 1} = 5}$

$\displaystyle \sf{ \therefore \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2} }$

Hence there is unique solution

We now find the solution

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

6x - y = 7 - - - - - - - - (2)

Equation 2 - 2 × Equation 1 gives

- 9y = - 9

⇒ y = 1

From Equation 1 we get

3x - 5 = - 1

⇒ 3x = 4

⇒ x = 4/3

FINAL ANSWER

The number of solutions of the pair of linear equations 3x - 5y = - 1 and 6x - y = 7 is unique and the solution is x = 4/3 , y = 1

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ Solve the given system of equations.

2x + 8y = 5 24x - 4y = -15

https://brainly.in/question/33685046

2. 2x+3y=12 and 4x+5y=22

https://brainly.in/question/18427922