Is it true to say that the pair of equations 4x 3y 12 and 2x 6y 2 has no solution Justify your answer 1?

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Solution:

Given, the pair of equations:

-x + 2y + 2 = 0

(1/2)x - (1/4)y - 1 = 0

We have to determine whether the pair of equations has a unique 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 \(\frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}}\), then the graph will be a pair of lines intersecting at a unique point, which is the solution of the pair of equations.

Here, a₁ = -1, b₁ = 2, c₁ = 2

a₂ = 1/2, b₂ = -1/4, c₂ = -1

So, a₁/a₂ = -1/(1/2) = -2

b₁/b₂ = 2/(-1/4) = -8

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

Therefore, the pair of equations has a unique solution.

✦ Try This: Determine if the pair of equations 2x - y = 0 and 3x + 7y = 0 has a unique solution or not.

Given, the pair of equations are

2x - y = 0

3x + 7y = 0

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

Here, a₁ = 2, b₁ = -1

a₂ = 3, b₂ = 7

So, a₁/a₂ = 2/3

b₁/b₂ = -1/7

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

Therefore, the pair of equations has a unique solution

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

NCERT Exemplar Class 10 Maths Exercise 3.2 Sample Problem 1

Summary:

The pair of equations -x + 2y + 2 = 0 and (1/2)x - (1/4)y - 1 = 0 has a unique solution

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