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2x + 4y = 3; 12y + 6x = 6, does this pair of linear equations have no solution

Solution:

Given, the pair of equations are

2x + 4y = 3

12y + 6x = 6

We have to determine whether the pair of equations has a solution or not.

We know that,

For a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,

If \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\), then

i) the pair of linear equation is inconsistent

ii) the graph will be a pair of parallel lines and so the pair of equations will have no solution.

The equation 12y + 6x = 6 can be rewritten as 6x + 12y = 6.

Here, a₁ = 2, b₁ = 4, c₁ = 3

a₂ = 6, b₂= 12, c₂= 6

So, a₁/a₂ = 2/6 = 1/3

b₁/b₂ = 4/12 = 1/3

c₁/c₂ = 3/6 = 1/2

1/3 = 1/3 ≠ 1/2

\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\)

Therefore, the pair of equations has no solution.

✦ Try This: Do the pair of linear equations 2x + 4y = 3; 8y + 4x = 9 have no solution? Justify your answer.

Given, the pair of equations are

2x + 4y = 3

8y + 4x = 9

We have to determine whether the pair of equations has a solution or not.

The equation 8y + 4x = 9 can be rewritten as 4x + 8y = 9.

Here, a₁ = 2, b₁ = 4, c₁ = 3

a₂ = 4, b₂ = 8, c₂ = 9

So, a₁/a₂ = 2/4 = 1/2

b₁/b₂ = 4/8 = 1/2

c₁/c₂ = 3/9 = 1/3

1/2 = 1/2 ≠ 1/3

\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\)

Therefore, the pair of equations has no solution.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.2 Problem 1 (i)

Summary:

The pair of linear equations 2x + 4y = 3; 12y + 6x = 6 has no solution.

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