Question

What is the solution of the pair of linear equation $2x+y=5,4x+2y=10$.

• A. No solution.
• B. Infinite many solution.
• C. Exactly two solutions
• D. Unique solution.

Answer 1

The correct option is B Infinite many solution.

The given system of equations is:

$2x+y–5=0$

$4x+2y–10=0$

The above equations are of the form

$a_{1}x+b_{1}y+c_1=0$

$a_{2}x+b_{2}y+c_2=0$

Here, $a_1$ = $2$, $b_1$ = $1$, $c_1$ = $-5$

$a_2$ = $4$, $b_2$ = $2$, $c_2$ = $-10$

So according to the question, we get
$\frac{a_1}{a_2}$ = $\frac{2}{4}$ = $\frac{1}{2}$

$\frac{b_1}{b_2}$ = $\frac{1}{2}$

$\frac{c_1}{c_2}$ = $\frac{-5}{-10}$= $\frac{1}{2}$

⇒ $\frac{a_1}{a_2}$ = $\frac{b_1}{b_2}$ = $\frac{c_1}{c_2}$

Hence, we can conclude that the given system of equation has infinity many solutions.