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{3}{2} x + \frac{5}{3} y = 7 \implies \frac{3}{2} x + \frac{5}{3} y - 7 = 0$$2) 9 x - 10 y = 14 \implies 9 x - 10 y -

Vedclass · Accepted Answer

Consistent

Vedclass · Answer

(A) Given equations are:$1) \frac{3}{2} x + \frac{5}{3} y = 7 \implies \frac{3}{2} x + \frac{5}{3} y - 7 = 0$$2) 9 x - 10 y = 14 \implies 9 x - 10 y - 14 = 0$Comparing with $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$:$a_{1} = \frac{3}{2}, b_{1} = \frac{5}{3}, c_{1} = -7$$a_{2} = 9, b_{2} = -10, c_{2} = -14$Now,calculating the ratios:$\frac{a_{1}}{a_{2}} = \frac{3/2}{9} = \frac{3}{18} = \frac{1}{6}$$\frac{b_{1}}{b_{2}} = \frac{5/3}{-10} = \frac{5}{-30} = -\frac{1}{6}$Since $\frac{a_{1}}{a_{2}} 
eq \frac{b_{1}}{b_{2}}$,the lines intersect at a unique point.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.
$\frac{3}{2} x + \frac{5}{3} y = 7$; $9 x - 10 y = 14$

Similar Questions

The pair of equations $2x + y = 3$ and $x + 2y = 4$ is:

The graph of a pair of lines $3x - 2y = 2$ and $6x - 4y = 4$ is.........

The intersection point in the graph of a pair of equations $x=0$ and $y=0$ is.........

Form the pair of linear equations in the following problems,and find their solutions graphically.
$5$ pencils and $7$ pens together cost ₹ $50$,whereas $7$ pencils and $5$ pens together cost ₹ $46$. Find the cost of one pencil and that of one pen.

Two straight paths are represented by the equations $x-3y=2$ and $-2x+6y=5$. Check whether the paths cross each other or not.

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