Coincident lines have infinite solutions. Which among the following pairs of lines are coincident?

x - y = 1

;

x + y = 1

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3 x = 5 + 2 y

;

y = 4 x + 1

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x = \frac{11}{5} - \frac{2 y}{5}; y = \frac{11}{2} - \frac{5 x}{2}

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x - y = 2

;

x + y = 2

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Solution

The correct option is C $x = \frac{11}{5} - \frac{2 y}{5}; y = \frac{11}{2} - \frac{5 x}{2}$
After converting the given pairs of equations to the general form
$a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ ,
it can be found that only for the pair $x = \frac{11}{5} - \frac{2 y}{5}$ ; $y = \frac{11}{2} - \frac{5 x}{2}, \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ , which is the condition for coincident lines with infinite solutions.

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Similar questions

Which of the following pairs of linear equations is inconsistent?
$1. x + 3 y - 5 = 0, 2 x + y = 0$
$2. 2 x + y = 1, 2 y = 2 - 4 x$
$3. 2 x - y = 2, 2 y - 4 x = 2$

Q. Question 11
x = 5 and y = 2 is a solution of the linear equation:

A) x + 2y = 7
B) 5x +2y = 7
C) x + y = 7
D) 5x + y = 7

Q. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

(i)

x + y = 5, 2 x + 2 y = 10

(ii)

x - y = 8, 3 x - 3 y = 16

(iii)

2 x + y - 6 = 0, 4 x - 2 y - 4 = 0

(iv)

2 x - 2 y - 2 = 0, 4 x - 4 y - 5 = 0

Q. Question 10
A pair of linear equations which has a unique solution x = 2 and y = - 3 is
(A) x + y = 1 and 2x – 3y = -5
(B) 2x + 5y = - 11 and 4x + 10y = - 22
(C) 2x – y = 1 and 3x + 2y = 0
(D) x – 4y + 14 = 0 and 5x – y – 13 = 0

Q. Classify the following pairs of lines as coincident, parallel or intersecting:
(i) 2x + y − 1 = 0 and 3x + 2y + 5 = 0
(ii) x − y = 0 and 3x − 3y + 5 = 0
(iii) 3x + 2y − 4 = 0 and 6x + 4y − 8 = 0.

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Coincident lines have infinite solutions. Which among the following pairs of lines are coincident?

The correct option is C x=115−2y5;y=112−5x2After converting the given pairs of equations to the general form a1x+b1y+c1=0 and a2x+b2y+c2=0, it can be found that only for the pair x=115−2y5 ; y=112−5x2,a1a2=b1b2=c1c2, which is the condition for coincident lines with infinite solutions.