On comparing the ratios frac{a_{1}}{a_{2}}, f | vedclass

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

Question

(A) Given equations are:$1) \frac{4}{3} x + 2 y - 8 = 0$$2) 2 x + 3 y - 12 = 0$Comparing with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{

Vedclass · Accepted Answer

Consistent

Vedclass · Answer

(A) Given equations are:$1) \frac{4}{3} x + 2 y - 8 = 0$$2) 2 x + 3 y - 12 = 0$Comparing with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$:$a_{1} = \frac{4}{3}, b_{1} = 2, c_{1} = -8$$a_{2} = 2, b_{2} = 3, c_{2} = -12$Calculating the ratios:$\frac{a_{1}}{a_{2}} = \frac{4/3}{2} = \frac{4}{6} = \frac{2}{3}$$\frac{b_{1}}{b_{2}} = \frac{2}{3}$$\frac{c_{1}}{c_{2}} = \frac{-8}{-12} = \frac{2}{3}$Since $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$,the lines are coincident.Because the lines are coincident,they have infinitely many solutions.Therefore,the pair of linear equations is consistent.

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:
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$

Similar Questions

Form the pair of linear equations in the following problems,and find their solutions graphically.
$10$ students of Class $X$ took part in a Mathematics quiz. If the number of girls is $4$ more than the number of boys,find the number of boys and girls who took part in the quiz.

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.
$\frac{3}{2} x + \frac{5}{3} y = 7$; $9 x - 10 y = 14$

Draw the graphs of the equations $5x - y = 5$ and $3x - y = 3$. Determine the coordinates of the vertices of the triangle formed by these lines and the $y$-axis.

Form the pair of linear equations in the following problems,and find their solutions (if they exist) by the elimination method.
The sum of the digits of a two-digit number is $9$. Also,nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}},$ find out whether the lines representing the following pairs of linear equations intersect at a point,are parallel,or are coincident:
$9x + 3y + 12 = 0$
$18x + 6y + 24 = 0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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:$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$