The pair of equations 2x + y - 4 = 0 and x + | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a pair of linear equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,the condition for a unique solution is $a_{1}/a_{2}

Vedclass · Accepted Answer

unique solution

Vedclass · Answer

(C) For a pair of linear equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,the condition for a unique solution is $a_{1}/a_{2} 
eq b_{1}/b_{2}$,which is equivalent to $a_{1}b_{2} - a_{2}b_{1} 
eq 0$.Here,$a_{1} = 2, b_{1} = 1, c_{1} = -4$ and $a_{2} = 1, b_{2} = 2, c_{2} = -5$.Calculating the determinant: $a_{1}b_{2} - a_{2}b_{1} = (2)(2) - (1)(1) = 4 - 1 = 3$.Since $3 
eq 0$,the pair of equations has a unique solution.

The pair of equations $2x + y - 4 = 0$ and $x + 2y - 5 = 0$ has........

Similar Questions

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}},$ find out whether the following pair of linear equations are consistent or inconsistent.
$5x - 3y = 11$; $-10x + 6y = -22$

Which of the following is a linear equation in two variables?

Draw the graphs of the pair of linear equations $x+3y=6$ and $2x-3y=12$. Determine the coordinates of the vertices of the triangle formed by these linear equations and the $Y$-axis.

$A$ line $2x - y = 6$ intersects the $X$-axis at........

Do the following equations represent a pair of coincident lines? Justify your answer.
$\frac{x}{2} + y + \frac{2}{5} = 0$
$4x + 8y + \frac{5}{16} = 0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module