Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
MediumSolve the following pair of linear equations by the substitution method.
$x+y=14$
$x-y=4$
$x+y=14$
$x-y=4$
(A) $x+y=14$ $....(1)$
$x-y=4$ $....(2)$
From equation $(1)$,we express $x$ in terms of $y$:
$x=14-y$ $....(3)$
Substituting the value of $x$ from equation $(3)$ into equation $(2)$:
$(14-y)-y=4$
$14-2y=4$
$14-4=2y$
$10=2y$
$y=5$ $....(4)$
Now,substituting the value of $y=5$ into equation $(3)$:
$x=14-5$
$x=9$
Therefore,the solution is $x=9$ and $y=5$.
$x-y=4$ $....(2)$
From equation $(1)$,we express $x$ in terms of $y$:
$x=14-y$ $....(3)$
Substituting the value of $x$ from equation $(3)$ into equation $(2)$:
$(14-y)-y=4$
$14-2y=4$
$14-4=2y$
$10=2y$
$y=5$ $....(4)$
Now,substituting the value of $y=5$ into equation $(3)$:
$x=14-5$
$x=9$
Therefore,the solution is $x=9$ and $y=5$.
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Similar Questions
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.
$3x + 2y = 5; \quad 2x - 3y = 7$
$3x + 2y = 5; \quad 2x - 3y = 7$
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 following pair of linear equations are consistent or inconsistent.
$\frac{3}{2} x + \frac{5}{3} y = 7$; $9 x - 10 y = 14$
$\frac{3}{2} x + \frac{5}{3} y = 7$; $9 x - 10 y = 14$
Easy
View SolutionSolve the pair of equations:
$\frac{2}{x} + \frac{3}{y} = 13$
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$\frac{2}{x} + \frac{3}{y} = 13$
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Difficult
View SolutionWhich of the following pairs of linear equations has a unique solution,no solution,or infinitely many solutions? In case there is a unique solution,find it by using the cross-multiplication method.
$x - 3y - 7 = 0$
$3x - 3y - 15 = 0$
$x - 3y - 7 = 0$
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Difficult
View SolutionGraphically,find whether the following pair of equations has no solution,unique solution or infinitely many solutions.
$5x - 8y + 1 = 0$ $...(1)$
$3x - \frac{24}{5}y + \frac{3}{5} = 6$ $...(2)$
$5x - 8y + 1 = 0$ $...(1)$
$3x - \frac{24}{5}y + \frac{3}{5} = 6$ $...(2)$
Medium
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