Question 3 (iv)
Are the following pair of linear equations consistent? Justify your answer
x + 3y = 11 and 2(2x + 6y) = 22

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Solution

x + 3y = 11 and 2x + 6y = 11
$a_{1} = 1, b_{1} = 3, c_{1} = - 11 a_{2} = 2, b_{2} = 6, c_{2} = - 11 n o w, \frac{a_{1}}{a_{2}} = \frac{1}{2}, \frac{b_{1}}{b_{2}} = \frac{3}{6} = \frac{1}{2}, \frac{c_{1}}{c_{2}} = \frac{- 11}{- 11} = 1 \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

The pair of equations represents a pair of parallel lines.
Hence, the pair of linear equations has no solution.

Thus, the pair of linear equations is inconsistent.

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Question 3 (iv)
On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ find out whether the following pair of linear equations are consistent, or inconsistent.
5x - 3y= 11 ; -10x+ 6y= -22

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Classification of Pair of Linear Equations

Standard X Mathematics

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Question 3 (iv) Are the following pair of linear equations consistent? Justify your answer x + 3y = 11 and 2(2x + 6y) = 22

x + 3y = 11 and 2x + 6y = 11 a1=1, b1=3, c1=−11a2=2, b2=6, c2=−11now, a1a2=12, b1b2=36=12,c1c2=−11−11=1a1a2=b1b2≠c1c2 The pair of equations represents a pair of parallel lines. Hence, the pair of linear equations has no solution. Thus, the pair of linear equations is inconsistent.

Question 3 (iv)
Are the following pair of linear equations consistent? Justify your answer
x + 3y = 11 and 2(2x + 6y) = 22