MCQ
The pair of equations $2x + y = 5, 3x + 2y = 8$ has:
- ✓A unique solution.
- BTwo solutions.
- CNo solution.
- DInfinitely 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.
$2x + y - 5 = 0$ 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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