(A) Given equations are:$5x - 4y + 8 = 0$$7x + 6y - 9 = 0$Comparing these equations with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x +

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(A) Given equations are:$5x - 4y + 8 = 0$$7x + 6y - 9 = 0$Comparing these equations with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,we obtain:$a_{1} = 5, b_{1} = -4, c_{1} = 8$$a_{2} = 7, b_{2} = 6, c_{2} = -9$Now,calculating the ratios:$\frac{a_{1}}{a_{2}} = \frac{5}{7}$$\frac{b_{1}}{b_{2}} = \frac{-4}{6} = -\frac{2}{3}$Since $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$,the lines representing the given pair of linear equations intersect at exactly one point.

Class 10 Mathematics Pair of Linear Equations in Two Variables Textbook - Pair of Linear Equations in Two Variables

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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:
$5x - 4y + 8 = 0$
$7x + 6y - 9 = 0$

A
Intersect at a point
B
Parallel
C
Coincident
D
None of these

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Textbook - Pair of Linear Equations in Two Variables

Solve by the method of substitution. Aftab tells his daughter,"Seven years ago,$I$ was seven times as old as you were then. Also,three years from now,$I$ shall be three times as old as you will be." Represent this situation algebraically.

Easy

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Solve the following pair of equations by reducing them to a pair of linear equations:
$\frac{4}{x} + 3y = 14$
$\frac{3}{x} - 4y = 23$

Medium

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Solve the following pair of linear equations by the substitution method:
$\frac{3x}{2} - \frac{5y}{3} = -2$
$\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$

Medium

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The sum of a two-digit number and the number obtained by reversing the digits is $66$. If the digits of the number differ by $2$,find the number. How many such numbers are there?

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Form the pair of linear equations for the following problem and find their solution by the substitution method: 'Five years hence,the age of Jacob will be three times that of his son. Five years ago,Jacob's age was seven times that of his son. What are their present ages?'

Medium

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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:$5x - 4y + 8 = 0$$7x + 6y - 9 = 0$

Similar Questions

Solve by the method of substitution. Aftab tells his daughter,"Seven years ago,$I$ was seven times as old as you were then. Also,three years from now,$I$ shall be three times as old as you will be." Represent this situation algebraically.

Solve the following pair of equations by reducing them to a pair of linear equations:$\frac{4}{x} + 3y = 14$$\frac{3}{x} - 4y = 23$

Solve the following pair of linear equations by the substitution method:$\frac{3x}{2} - \frac{5y}{3} = -2$$\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$

The sum of a two-digit number and the number obtained by reversing the digits is $66$. If the digits of the number differ by $2$,find the number. How many such numbers are there?

Form the pair of linear equations for the following problem and find their solution by the substitution method: 'Five years hence,the age of Jacob will be three times that of his son. Five years ago,Jacob's age was seven times that of his son. What are their present ages?'

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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:
$5x - 4y + 8 = 0$
$7x + 6y - 9 = 0$

Solve the following pair of equations by reducing them to a pair of linear equations:
$\frac{4}{x} + 3y = 14$
$\frac{3}{x} - 4y = 23$

Solve the following pair of linear equations by the substitution method:
$\frac{3x}{2} - \frac{5y}{3} = -2$
$\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$