Question

The pair of linear equations 2x+y-5-0 and 3x-2y-4=0 intersect at the point.

• A. (1,2)
• B. (2,1)
• C. (1,3)
• D. (1,-1)

Answer 1

The Correct Option is B

We are tasked with finding the point of intersection of the pair of linear equations:

\[ 2x + y - 5 = 0 \quad \text{and} \quad 3x - 2y - 4 = 0. \]

Step 1: Solve the system of equations.

Rewrite the equations in standard form:

\[ y = 5 - 2x \quad \text{(from the first equation)}. \]

Substitute \( y = 5 - 2x \) into the second equation:

\[ 3x - 2(5 - 2x) - 4 = 0. \]

Simplify:

\[ 3x - 10 + 4x - 4 = 0 \implies 7x - 14 = 0 \implies x = 2. \]

Substitute \( x = 2 \) into \( y = 5 - 2x \):

\[ y = 5 - 2(2) = 5 - 4 = 1. \]

Final Answer: The point of intersection is \( \mathbf{(2, 1)} \), which corresponds to option \( \mathbf{(2)} \).