Is the pair of equations x + 2y - 3 = 0 and 6y + 3x - 9 = 0 consistent? Justify your answer
Solution:
Given, the pair of equations is
x + 2y - 3 = 0
6y + 3x - 9 = 0
We have to determine if the pair of equations is consistent.
We know that,
A pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 is dependent and consistent, if \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\) and the graph will be a pair of coincident lines.
The equation 6y + 3x - 9 = 0 can be rewritten as 3x + 6y - 9 = 0
Here, a₁ = 1, b₁ = 2, c₁ = -3
a₂ = 3, b₂ = 6, c₂ = -9
So, a₁/a₂ = 1/3
b₁/b₂ = 2/6 = 1/3
c₁/c₂ = -3/-9 = 1/3
\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{3}\)
Therefore, the pair of equations is consistent.
✦ Try This: Is the pair of equations 3x + 2y - 6 = 0 and 6x + 4y - 12 = 0 consistent? Justify your answer.
Given, the pair of equations are
3x + 2y - 6 = 0
6x + 4y - 12 = 0
We have to determine if the pair of equations is consistent.
Here, a₁ = 3, b₁ = 2, c₁ = -6
a₂ = 6, b₂ = 4, c₂ = -12
So, a₁/a₂ = 3/6 = 1/2
b₁/b₂ = 2/4 = 1/2
c₁/c₂ = -6/-12 = 1/2
\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{3}\)
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 Sample Problem 3
Is the pair of equations x + 2y - 3 = 0 and 6y + 3x - 9 = 0 consistent? Justify your answer
Summary:
The pair of equations x + 2y - 3 = 0 and 6y + 3x - 9 = 0 is consistent.
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