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- 3x - 4y = 12; 4y + 3x = 12, are these pair of linear equations consistent

Solution:

Given, the pair of equations are

-3x - 4y = 12

4y + 3x = 12

We have to determine if the pair of linear equations are consistent.

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 the pair of linear equation is inconsistent

The equation 4y + 3x = 12 can be written as 3x + 4y = 12.

Here, a₁ = -3, b₁ = -4, c₁= 12

a₂ = 3, b₂ = 4, c₂ = 12

So, a₁/a₂ = -3/3 = -1

b₁/b₂ = -4/4 = -1

c₁/c₂ = 12/12 = 1

-1 = -1 ≠ 1

Therefore, the pair of linear equations is inconsistent.

✦ Try This: Are the following pair of linear equations consistent? Justify your answer

3x - 4y = 12; -3x + 4y = -12

Given, the pair of equations are

3x - 4y = 12

-3x + 4y = -12

We have to determine if the pair of linear equations is consistent.

We know that,

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

If \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\), then the pair of linear equation is consistent.

Here, a₁ = 3, b₁ = -4, c₁ = 12

a₂ = -3, b₂ = 4, c₂ = -12

So, a₁/a₂ = -3/3 = -1

b₁/b₂ = -4/4 = -1

c₁/c₂ = 12/-12 = -1

-1 = -1 = -1

Therefore, the pair of equations is consistent

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

NCERT Exemplar Class 10 Maths Exercise 3.2 Problem 3 (i)

Summary:

The pair of linear equations - 3x - 4y = 12; 4y + 3x = 12 is not consistent.

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