Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
MediumUse the elimination method to find all possible solutions of the following pair of linear equations:
$2x + 3y = 8$ $...(1)$
$4x + 6y = 7$ $...(2)$
$2x + 3y = 8$ $...(1)$
$4x + 6y = 7$ $...(2)$
(D) Step $1$: Multiply Equation $(1)$ by $2$ and Equation $(2)$ by $1$ to make the coefficients of $x$ equal. Then we get the equations as:
$4x + 6y = 16$ $...(3)$
$4x + 6y = 7$ $...(4)$
Step $2$: Subtracting Equation $(4)$ from Equation $(3)$:
$(4x - 4x) + (6y - 6y) = 16 - 7$
i.e.,$0 = 9$,which is a false statement.
Therefore,the pair of linear equations has no solution.
$4x + 6y = 16$ $...(3)$
$4x + 6y = 7$ $...(4)$
Step $2$: Subtracting Equation $(4)$ from Equation $(3)$:
$(4x - 4x) + (6y - 6y) = 16 - 7$
i.e.,$0 = 9$,which is a false statement.
Therefore,the pair of linear equations has no solution.
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Similar Questions
Solve the following pair of equations by reducing them to a pair of linear equations:
$\frac{4}{x} + 3y = 14$
$\frac{3}{x} - 4y = 23$
$\frac{4}{x} + 3y = 14$
$\frac{3}{x} - 4y = 23$
Medium
View SolutionOn 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:
$5x - 4y + 8 = 0$
$7x + 6y - 9 = 0$
$5x - 4y + 8 = 0$
$7x + 6y - 9 = 0$
Easy
View SolutionSolve the following pair of equations by reducing them to a pair of linear equations:
$\frac{1}{3x+y} + \frac{1}{3x-y} = \frac{3}{4}$
$\frac{1}{2(3x+y)} - \frac{1}{2(3x-y)} = -\frac{1}{8}$
$\frac{1}{3x+y} + \frac{1}{3x-y} = \frac{3}{4}$
$\frac{1}{2(3x+y)} - \frac{1}{2(3x-y)} = -\frac{1}{8}$
Difficult
View SolutionForm 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.
$10$ 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.
Difficult
View SolutionOn 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:
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$
Medium
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