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Q3(i):
Form the pair of linear equations for the following problems and find their solution by substitution method. (i) The difference between two numbers is 26 and one number is three times the other. Find them.
Solution :
Given:
1. The difference between two numbers is $26$.
2. One number is three times the other number.
To Find:
The two numbers.
Step 1: Defining the Variables
Let the larger number be $x$.
Let the smaller number be $y$.
Step 2: Formulating the Linear Equations
Based on the given conditions, we can form the following system of linear equations:
Equation (1): $x - y = 26$ [Since the difference between the two numbers is 26]
Equation (2): $x = 3y$ [Since one number is three times the other]
Step 3: Applying the Substitution Method
The substitution method involves substituting the value of one variable from one equation into the other equation.
We already have $x$ expressed in terms of $y$ in Equation (2): $x = 3y$.
Substitute $x = 3y$ into Equation (1):
$(3y) - y = 26$
Step 4: Solving for $y$
Simplify the expression:
$2y = 26$
Divide both sides by $2$:
$y = \frac{26}{2}$
$y = 13$
Step 5: Solving for $x$
Now, substitute the value of $y = 13$ back into Equation (2) to find $x$:
$x = 3y$
$x = 3(13)$
$x = 39$
Step 6: Verification
Check the results against the original conditions:
Difference: $39 - 13 = 26$ (Condition 1 satisfied)
Ratio: $39 = 3 \times 13$ (Condition 2 satisfied)
Final Answer: The two numbers are 39 and 13.
More Questions from Class 10 Mathematics Pair of linear equations in two variable EXERCISE 3.2
- Q1(i): Solve the following pair of linear equations by the substitution method. (i) x + y = 14; x – y = 4
- Q1(ii): Solve the following pair of linear equations by the substitution method. (ii) s – t = 3; $\frac{s}{3} + \frac{t}{2} = 6$
- Q1(iii): Solve the following pair of linear equations by the substitution method. (iii) 3x – y = 3; 9x – 3y = 9
- Q1(iv): Solve the following pair of linear equations by the substitution method. (iv) 0.2x + 0.3y = 1.3; 0.4x + 0.5y = 2.3
- Q1(v): Solve the following pair of linear equations by the substitution method. (v) $\sqrt{2}x + \sqrt{3}y = 0$; $\sqrt{3}x - \sqrt{8}y = 0$
- Q1(vi): Solve the following pair of linear equations by the substitution method. (vi) $\frac{3x}{2} - \frac{5y}{3} = -2$; $\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$
- Q2: Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘$m$’ for which y = mx + 3.
- Q3(ii): Form the pair of linear equations for the following problems and find their solution by substitution method. (ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
- Q3(iii): Form the pair of linear equations for the following problems and find their solution by substitution method. (iii) The coach of a cricket team buys 7 bats and 6 balls for ` 3800. Later, she buys 3 bats and 5 balls for ` 1750. Find the cost of each bat and each ball.
- Q3(iv): Form the pair of linear equations for the following problems and find their solution by substitution method. (iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ` 105 and for a journey of 15 km, the charge paid is ` 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
- Q3(v): Form the pair of linear equations for the following problems and find their solution by substitution method. (v) A fraction becomes $\frac{9}{11}$, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$. Find the fraction.
- Q3(vi): Form the pair of linear equations for the following problems and find their solution by substitution method. (vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
CBSE Solutions for Class 10 Mathematics Pair of linear equations in two variable
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