Examine graphically whether the pair of equat | vedclass

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

Question

(A) To check if the pair of equations is consistent,we compare the ratios of the coefficients: $a_1 = 2, b_1 = 4, c_1 = -9$ $a_2 = 3, b_2 = 6, c_2 = -

Vedclass · Accepted Answer

Consistent

Vedclass · Answer

(A) To check if the pair of equations is consistent,we compare the ratios of the coefficients: $a_1 = 2, b_1 = 4, c_1 = -9$ $a_2 = 3, b_2 = 6, c_2 = -\frac{27}{2}$ Calculating the ratios: $\frac{a_1}{a_2} = \frac{2}{3}$ $\frac{b_1}{b_2} = \frac{4}{6} = \frac{2}{3}$ $\frac{c_1}{c_2} = \frac{-9}{-27/2} = \frac{9 	imes 2}{27} = \frac{18}{27} = \frac{2}{3}$ Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} = \frac{2}{3}$,the lines are coincident. Coincident lines have infinitely many solutions,therefore the system is consistent.

Examine graphically whether the pair of equations $2x + 4y = 9$ and $3x + 6y = \frac{27}{2}$ is consistent.

Similar Questions

Solve the following pair of equations by the method of cross multiplication:
$ax + by - a + b = 0$
$bx - ay - a - b = 0$

The pair of equations $x=a$ and $y=b$ graphically represents lines which are

Solve the following pair of equations by the cross-multiplication method:
$\frac{x}{a} - \frac{y}{b} = 0$
$ax + by = a^2 + b^2$

The sum of the digits of a two-digit number is $9$. The number obtained by interchanging the digits exceeds the original number by $45$. Find the original number.

Solve the following pair of equations by the cross-multiplication method:
$\frac{x}{a} + \frac{y}{b} = a + b$
$\frac{x}{a^2} + \frac{y}{b^2} = 2$

Vedclass Test Series

Exam Paper Generator

Online Exam Module