The sum of two numbers is 35 and their difference is 13. Formulate a pair of linear equations and find the numbers.

Q: The sum of two numbers is 35 and their difference is 13. Formulate a pair of linear equations and find the numbers.

Let the two required numbers be $x$ and $y$, where $x > y$. \nAccording to the first given condition: $$x + y = 35$$ --- (Equation 1) \nAccording to the second condition: $$x - y = 13$$ --- (Equation 2) \nAdding Equation 1 and Equation 2: $$(x + y) + (x - y) = 35 + 13$$ $$2x = 48 \implies x = 24$$ \nNow substituting $x = 24$ into Equation 1: $$24 + y = 35 \implies y = 35 - 24 \implies y = 11$$ \nThus, the two required numbers are 24 and 11, satisfying both given conditions.

Question

Accepted Answer

Let the two required numbers be $x$ and $y$, where $x > y$. 
According to the first given condition: $$x + y = 35$$ --- (Equation 1) 
According to the second condition: $$x - y = 13$$ --- (Equation 2) 
Adding Equation 1 and Equation 2: $$(x + y) + (x - y) = 35 + 13$$ $$2x = 48 \implies x = 24$$ 
Now substituting $x = 24$ into Equation 1: $$24 + y = 35 \implies y = 35 - 24 \implies y = 11$$ 
Thus, the two required numbers are 24 and 11, satisfying both given conditions.

NCERT · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesThe sum of two numbers is 35 and their difference is 13. Formulate a pair of linear equations and find the numbers.