Find the best tutors and institutes for Class 10 Tuition
Q2:
Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘$m$’ for which y = mx + 3.
Solution :
Given: A system of two linear equations in two variables:
(i) $2x + 3y = 11$
(ii) $2x - 4y = -24$
Additionally, a linear relation: $y = mx + 3$.
To Find: The values of $x$ and $y$ that satisfy the system of equations, and subsequently, the value of the constant $m$.
Step 1: Solving the system of linear equations using the Elimination Method.
We have the system:
$2x + 3y = 11$ --- (Equation 1)
$2x - 4y = -24$ --- (Equation 2)
To eliminate the variable $x$, we subtract Equation 2 from Equation 1:
$(2x + 3y) - (2x - 4y) = 11 - (-24)$
$2x + 3y - 2x + 4y = 11 + 24$ [Distributing the negative sign]
$7y = 35$ [Combining like terms: $2x - 2x = 0$ and $3y + 4y = 7y$]
$y = \frac{35}{7}$ [Dividing both sides by 7]
$y = 5$
Step 2: Finding the value of $x$.
Substitute the value $y = 5$ into Equation 1:
$2x + 3(5) = 11$
$2x + 15 = 11$ [Performing multiplication]
$2x = 11 - 15$ [Transposing 15 to the right side]
$2x = -4$
$x = \frac{-4}{2}$ [Dividing both sides by 2]
$x = -2$
Step 3: Finding the value of $m$.
We are given the equation $y = mx + 3$. Substitute $x = -2$ and $y = 5$ into this equation:
$5 = m(-2) + 3$
$5 = -2m + 3$
$5 - 3 = -2m$ [Transposing 3 to the left side]
$2 = -2m$
$m = \frac{2}{-2}$ [Dividing both sides by -2]
$m = -1$
Final Answer: The solution to the system is $x = -2$ and $y = 5$. The value of $m$ for which $y = mx + 3$ is $m = -1$.
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) $\frac{3x}{2} - \frac{5y}{3} = -2$; $\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$
- 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(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
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Pair of linear equations in two variable
I was a working professional .Left my job and started teaching as a tutor. I have been a national level debater . I am a famous teacher amongst my students .
Class 10 is a pivotal, fast-paced school year filled with a mix of academic preparation, growing responsibilities, and memorable moments with friends.Daily Routine and StudiesBusy schedules: Days involve attending subject-specific classes, taking detailed notes, and preparing for board exams.Favorite subjects: Time is often spent engaging deeply with core subjects like mathematics, science, and social studies.Extra help: Teachers provide extra guidance and revision sessions to help students handle exam stress.Friendships and Social LifeStronger bonds: Friendships deepen through shared lunch breaks, group studies, and mutual support during exams.Lasting memories: Small moments in the hallway or sharing stories in the classroom create a sense of a second family.
An accommodating and versatile individual with the talent to develop inspiring hands-on lessons that will capture a child's imagination and breed success.
I have volunteer teacher for evidyaloka ..I thought higg school students math and science
Over 6+ years, I've honed my craft as a mentor and educator to more than 100s of students, catalyzing their academic and personal development. My approach goes beyond traditional teaching, integrating experiential learning and technology to engage students and deepen comprehension. Through individualized attention and encouragement, I've guided countless students to exceed expectations, fostering a culture of achievement and self-discovery. Witnessing their transformative journeys, from overcoming challenges to embracing their potential, has been profoundly rewarding.
Vijay Sir's teaching style is effective and enjoyable. He uses real-world examples that make Grade 10 Maths and Science extremely relatable. I always look forward to his class.
Find more Tutor for Pair of linear equations in two variable in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 10 Mathematics Pair of linear equations in two variable EXERCISE 3.2 worksheets
Download Now