State the condition for one solution, infinite solutions and no solution for a pair of linear equations.

Open in App

Solution

We have two linear equations
$a_{1} x + b_{1} y + c_{1} = 0 - - - - - - - - - - (1)$
$a_{2} x + b_{2} y + c_{2} = 0 - - - - - - - - - - (2)$

Condition for exactly one solution= $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

Condition for infinite solutions = $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

Condition for no solution = $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Suggest Corrections

255

Similar questions

a_{1} x + b_{1} y + c_{1} = 0

a_{2} x + b_{2} y + c_{2} = 0

λ

λ x + y = λ^{2}

x + λ y = 1

For a pair of linear equation $a_{1}$ =12, $b_{1}$ = 2, $c_{1}$ = 6 and $a_{2}$ =24, $b_{2}$ =4, $c_{2}$ =7 ; the linear equation has

Join BYJU'S Learning Program