(A) Given equations are:$x + 2y = 5$ --- $(1)$$3x + 5y = 13$ --- $(2)$To solve by elimination,multiply equation $(1)$ by $3$:$3(x + 2y) = 3(5)$$3x +

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(A) Given equations are:$x + 2y = 5$ --- $(1)$$3x + 5y = 13$ --- $(2)$To solve by elimination,multiply equation $(1)$ by $3$:$3(x + 2y) = 3(5)$$3x + 6y = 15$ --- $(3)$Subtract equation $(2)$ from equation $(3)$:$(3x + 6y) - (3x + 5y) = 15 - 13$$y = 2$Substitute $y = 2$ into equation $(1)$:$x + 2(2) = 5$$x + 4 = 5$$x = 5 - 4$$x = 1$Thus,the solution is $x = 1, y = 2$.

Class 10 Mathematics Pair of Linear Equations in Two Variables Mix Examples - Pair of Linear Equations in Two Variables

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The solution of the pair of equations $x + 2y = 5$ and $3x + 5y = 13$ is ...........

A
$x = 1, y = 2$
B
$x = 2, y = 1$
C
$x = -1, y = -2$
D
$x = 2, y = -1$

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

Solve the following pairs of linear equations: $\frac{5}{a} - \frac{6}{b} = 3$ and $\frac{1}{a} + \frac{4}{b} = 11$.

Medium

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The sum of two positive numbers is $25$. Five times the smaller number is $5$ more than three times the larger number. Represent this as a pair of linear equations in two variables.

Medium

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The solution of a pair of equations $y+x=2$ and $y-x=4$ is $(x, y)=\ldots \ldots \ldots . . .$

Easy

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If $(1, y)$ is the solution of the linear equation of two variables $2x + 3y = 8$,then $y = \ldots$

Easy

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In $\Delta ABC$,$m \angle A = x$,$m \angle B = 3x$,and $m \angle C = y$. If $3y - 5x = 30$,show that the triangle is right-angled and find the measures of all three angles.

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The solution of the pair of equations $x + 2y = 5$ and $3x + 5y = 13$ is ...........

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Solve the following pairs of linear equations: $\frac{5}{a} - \frac{6}{b} = 3$ and $\frac{1}{a} + \frac{4}{b} = 11$.

The sum of two positive numbers is $25$. Five times the smaller number is $5$ more than three times the larger number. Represent this as a pair of linear equations in two variables.

The solution of a pair of equations $y+x=2$ and $y-x=4$ is $(x, y)=\ldots \ldots \ldots . . .$

If $(1, y)$ is the solution of the linear equation of two variables $2x + 3y = 8$,then $y = \ldots$

In $\Delta ABC$,$m \angle A = x$,$m \angle B = 3x$,and $m \angle C = y$. If $3y - 5x = 30$,show that the triangle is right-angled and find the measures of all three angles.

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