The system of linear equations 3x + y + 4 = 0 and 2x + y + 9 = 0 has: Option 1: No Solution Option 2: Unique Solution Option 3: Infinite Many Solution Option 4: Solution can not be predicted

Answer: Unique Solution. Solution: Compare the coefficients: a_1/a_2 = 3/2 and b_1/b_2 = 1/1. Since 3/2 ≠ 1/1, the lines are not parallel and intersect at exactly one point. Subtracting gives x = -5 and y = 11, a unique solution.

Quantitative Reasoning

Linear Equation

Easy

The system of linear equations 3x + y + 4 = 0 and 2x + y + 9 = 0 has:

No Solution

Unique Solution

Infinite Many Solution

Solution can not be predicted

✅ Correct Option: 2

Compare the coefficients: $\frac{a_1}{a_2} = \frac{3}{2}$ and $\frac{b_1}{b_2} = \frac{1}{1}$ .

Since $\frac{3}{2} \neq \frac{1}{1}$ , the lines are not parallel and intersect at exactly one point.

Subtracting gives $x = -5$ and $y = 11$ , a unique solution.

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The distance between origin and the point of intersection of lines x + y – 5 = 0 and x – y + 1 = 0, is:

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Match List I with List II

	LIST I (Equations)		LIST II (Solutions)
A.	$2x - 4 = 2 - x$	I.	$x = 3$
B.	$7 - 4x = 0$	II.	$x = 2$
C.	$\frac{x}{2} - 3 = 0$	III.	$x = \frac{7}{4}$
D.	$2x + 3 = x + 6$	IV.	$x = 6$

Choose the correct answer from the options given below:

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Which one of the following pairs of linear equations is/are inconsistent?

(A). $7x + y = 5, 14x + 2y = 10$

(B). $2x - 3y = 7, 4x - 6y = 12$

(C). $x - y = 10, 3x - 3y = 16$

(D). $2x - 2y - 2 = 0, 4x - 4y - 5 = 0$

Choose the correct option from the given below:

The system of linear equations 3x + y + 4 = 0 and 2x + y + 9 = 0 has:

Solution

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