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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.
Solution :
Given:
1. Two angles are supplementary, meaning their sum is $180^\circ$.
2. The larger angle exceeds the smaller angle by $18^\circ$.
To Find:
The measures of the two angles.
Step 1: Defining Variables
Let the larger angle be $x$ degrees.
Let the smaller angle be $y$ degrees.
Step 2: Formulating the Equations
Based on the property of supplementary angles:
$x + y = 180$ --- (Equation 1)
Based on the condition that the larger angle exceeds the smaller by $18^\circ$:
$x = y + 18$ --- (Equation 2)
Step 3: Solving by Substitution Method
We already have $x$ expressed in terms of $y$ in Equation 2. We substitute this expression for $x$ into Equation 1.
Substitute $(y + 18)$ for $x$ in Equation 1:
$(y + 18) + y = 180$
[Combining like terms $y$ and $y$]:
$2y + 18 = 180$
[Subtracting 18 from both sides of the equation]:
$2y = 180 - 18$
$2y = 162$
[Dividing both sides by 2]:
$y = \frac{162}{2}$
$y = 81$
Step 4: Finding the value of $x$
Now, substitute the value of $y = 81$ back into Equation 2:
$x = y + 18$
$x = 81 + 18$
$x = 99$
Step 5: Verification
Check if the sum is $180^\circ$: $99^\circ + 81^\circ = 180^\circ$. (Correct)
Check if the difference is $18^\circ$: $99^\circ - 81^\circ = 18^\circ$. (Correct)
Final Answer: The larger angle is $99^\circ$ and the smaller angle is $81^\circ$.
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(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.
- 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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