The pair of equations 2x + y = 5, 3x + 2y = 8 has: - Vidyadip

MCQ

The pair of equations 2x + y = 5, 3x + 2y = 8 has:

✓
A unique solution.
B
Two solutions.
C
No solution.
D
Infinitely many solutions.

✓

Answer

Correct option: A.

A unique solution.

The given system of equations can be written can be follows:
2x + y - 5 = 0 and 3x + 2y - 8 = 0
The given equations are of the following form:
ax + by + c = 0 and ax + by + c = 0
Here, a = 2, b = 1, c = -5 and a = 3, b = 2 and c = -8
$\therefore\frac{\text{a}_1}{\text{a}_2}=\frac{2}{3},\ \frac{\text{b}_1}{\text{b}_2}=\frac{1}{2}$ and $\frac{\text{c}_1}{\text{c}_2}=\frac{-5}{-8}=\frac{5}{8}$
$\therefore\frac{\text{a}_1}{\text{a}_2}\neq\frac{\text{b}_1}{\text{b}_2}$
The given system has a unique solution.
Hence, the lines intersect at one point.

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