Question

Fill in the blank:
The pair of equations $2x+3y=2$ and $4x+6y=1$ have ________.

• A. Exactly one solution
• B. No solution
• C. Infinitely many solutions
• D. Two solutions

Answer 1

The correct option is B No solution

The general form for a pair of linear equations in two variables $x$ and $y$ is
$a_{1}x+b_{1}y+c_1=0$ and
$a_{2}x+b_{2}y+c_2=0$
$2x+3y=2$ .....(1)
$4x+6y=1$ .....(2)
Comparing equations (1) and (2) with the general form of equation to write their co-efficient,
$a_1=2;a_2=4;b_1=3;b_2=6;c_1=2;c_2=1$
Compare the ratio,$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\frac{2}{4}=\frac{3}{6}=\frac{2}{1}$
If $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$, then the pair of linear equations has no solution.