(A) Let the larger number be $x$ and the smaller number be $y$.According to the first condition,$x = y + 3$ or $x - y = 3$ (Equation $1$).According to

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(A) Let the larger number be $x$ and the smaller number be $y$.According to the first condition,$x = y + 3$ or $x - y = 3$ (Equation $1$).According to the second condition,$2x + 17 = 3y$ or $2x - 3y = -17$ (Equation $2$).Substitute $x = y + 3$ into Equation $2$:$2(y + 3) - 3y = -17$$2y + 6 - 3y = -17$$-y + 6 = -17$$-y = -23$$y = 23$.Now,find $x$ using $x = y + 3$:$x = 23 + 3 = 26$.Therefore,the numbers are $26$ and $23$.

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

Medium

$A$ number is $3$ less than another number. By adding $17$ to twice the larger number,it becomes thrice the smaller number. Find these numbers.

A
$26, 23$
B
$62, 20$
C
$20, 27$
D
$29, 21$

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Mix Examples - Pair of Linear Equations in Two Variables

Solve the following pair of linear equations:
$21x + 47y = 110$
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The father's age is six times his son's age. Four years hence,the age of the father will be four times his son's age. The present ages,in years,of the son and the father are,respectively

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$A$ number is $3$ less than another number. By adding $17$ to twice the larger number,it becomes thrice the smaller number. Find these numbers.

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Solve the following pair of linear equations:$21x + 47y = 110$$47x + 21y = 162$

Draw the graphs of the pair of linear equations $x+y=10$ and $x-y=4$. Determine the coordinates of the vertices of the triangle formed by these linear equations and the $X$-axis.

Five years ago,the sum of the ages of a father and two sons was $x$ years. Then,after five years,the sum of the ages of all will be $\ldots \ldots \ldots$ years.

For a pair of equations $2x + 3y = 1$ and $3x - 2y = 8$,in usual notations $a_{1}b_{2} - a_{2}b_{1} = \dots$

The father's age is six times his son's age. Four years hence,the age of the father will be four times his son's age. The present ages,in years,of the son and the father are,respectively

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Solve the following pair of linear equations:
$21x + 47y = 110$
$47x + 21y = 162$