Question

write the number of solutions for the following pair of linear equation X+3y-4=0 ,2x+6y=7​

Answer 1

Answer:

hlo

Step-by-step explanation:

please follow me

mark as brainlist

Answer 2

The pair of equations x + 3y - 4 = 0 and 2x + 6y = 7 have no solutions

Given :

The pair of equations x + 3y - 4 = 0 and 2x + 6y = 7

To find :

The number of solutions of the pair of equations

Concept :

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

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

Solution :

Step 1 of 2 :

Write down the given pair of equations

Here the given pair of linear equations are

x + 3y - 4 = 0 and 2x + 6y = 7

Which can be rewritten as

x + 3y - 4 = 0 - - - - - (1)

2x + 6y - 7 = 0 - - - - - (2)

Step 2 of 2 :

Find the number of solutions

x + 3y - 4 = 0 - - - - - (1)

2x + 6y - 7 = 0 - - - - - (2)

Comparing with the equations

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

a₁ = 1 , b₁ = 3 , c₁ = - 4 and a₂ = 2 , b₂ = 6 , c₂ = - 7

Now we have ,

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

$\displaystyle \sf \frac{b_1}{b_2} = \frac{3}{ 6} = \frac{1}{2}$

$\displaystyle \sf \frac{c_1}{c_2} = \frac{ - 4}{ - 7} = - \frac{4}{7}$

Thus we get ,

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

Hence the pair of equations x + 3y - 4 = 0 and 2x + 6y = 7 have no solutions

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ how many solution does the pair of equations 3x + 4y + 2 = 0 , 4x = 5y - 13 have ? give reason

https://brainly.in/question/4061875

2. the pair of equations 3x-5y=7 and -6x+10y=7 has

https://brainly.in/question/17643487

#SPJ3