(A) Let the length of the rectangle be $x$ and the width be $y$.According to the problem,the length is $3$ less than twice the width,so $x = 2y - 3$,w

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(A) Let the length of the rectangle be $x$ and the width be $y$.According to the problem,the length is $3$ less than twice the width,so $x = 2y - 3$,which can be written as $x - 2y + 3 = 0$.The perimeter of a rectangle is given by $2(x + y) = 100$.Dividing both sides by $2$,we get $x + y = 50$.Thus,the pair of linear equations is $x - 2y + 3 = 0$ and $x + y = 50$.

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

Medium

In a rectangle,the length is $3$ less than twice its width. The perimeter of the rectangle is $100$. Represent this situation as a pair of linear equations in two variables.

A
$x - 2y + 3 = 0, x + y = 50$
B
$x - 2y - 3 = 0, x + y = 50$
C
$x + 2y - 3 = 0, x + y = 100$
D
$x - 2y + 3 = 0, x + y = 100$

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

The solution set of a pair of equations $x=4$ and $y=5$ is $\ldots \ldots \ldots \ldots$

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In a two-digit number, the digit at the unit's place is $x$ and the digit at the ten's place is $2x$. Then, the number is..........

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Comparing the equation $y = -3$ with the standard form $ax + by + c = 0$,we get $a = \dots$

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Solve the following pair of linear equations by the method of elimination:
$4x - 3y = 8$
$6x - y = \frac{29}{3}$

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Which of the following groups truly matches the data of Part $I$ with the data of Part $II$?

Part $I$ Part $II$

$1.$ The solution of $2x - y = 4$ and $3x - 2y = 5$ $a.$ $x = 3, y = 2$

$2.$ The solution of $5x - y = 14$ and $4x - 3y = 9$ $b.$ $x = 3, y = 1$

$3.$ The solution of $4x - 3y = 5$ and $3x - y = 5$ $c.$ $x = 2, y = 1$

$4.$ The solution of $3x - 2y = -1$ and $2x - 5y = -8$ $d.$ $x = 1, y = 2$

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Part $I$	Part $II$
$1.$ The solution of $2x - y = 4$ and $3x - 2y = 5$	$a.$ $x = 3, y = 2$
$2.$ The solution of $5x - y = 14$ and $4x - 3y = 9$	$b.$ $x = 3, y = 1$
$3.$ The solution of $4x - 3y = 5$ and $3x - y = 5$	$c.$ $x = 2, y = 1$
$4.$ The solution of $3x - 2y = -1$ and $2x - 5y = -8$	$d.$ $x = 1, y = 2$

In a rectangle,the length is $3$ less than twice its width. The perimeter of the rectangle is $100$. Represent this situation as a pair of linear equations in two variables.

Similar Questions

The solution set of a pair of equations $x=4$ and $y=5$ is $\ldots \ldots \ldots \ldots$

In a two-digit number, the digit at the unit's place is $x$ and the digit at the ten's place is $2x$. Then, the number is..........

Comparing the equation $y = -3$ with the standard form $ax + by + c = 0$,we get $a = \dots$

Solve the following pair of linear equations by the method of elimination:$4x - 3y = 8$$6x - y = \frac{29}{3}$

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Solve the following pair of linear equations by the method of elimination:
$4x - 3y = 8$
$6x - y = \frac{29}{3}$