HOTS Questions: Pair of Linear Equations in Two Variables

# HOTS Questions: Pair of Linear Equations in Two Variables - Mathematics (Maths) Class 10

Q1. If two of the roots of f(x) = x3 – 5x2 – 16x + 80 are equal in magnitude but opposite in sign, then find all of its zeroes.

Hint: Let α and β are the two zeroes which are equal in magnitude but opposite in sign.
∴ α + β = 0
(Let the third zero is γ)
Sum of zeroes of
f(x)= α + β + γ  =
∴ γ = 5  [α + β = 0]
Product of zeroes

⇒ – α2 = –16  [α + β = 0 ⇒ β = – α]
⇒ α2 = 16   ⇒  α = ± 4
α = ± 4 ⇒ β = ∓ 4
[∴ β = –α]
Thus, the zeroes are : [± 4, ∓ 4, and 5]

Q2.
Hint:

Adding (1) and (2), we get x = 1/3 and y = 1/2
Q3. Solve :

Hint: Put x + 2y = p and 2x – y = q
We have      ...(1)
...(2)
Solving (1) and (2), we get p = 4 and q = 3
∴ x + 2y = 4  and 2x – y = 3
Solving these equations, we get x = 2 and y = 1

Q4. Solve : x + y = 18 ; y + z  = 12 ;  z + x = 16.
Hint: Adding the three equations, we get

⇒ x + y + z  = 23
Now, (x + y + z = 23) – (x + y = 18)
⇒ z = 5 (x + y + z = 23) – (y + z = 12)
⇒ x = 11 (x + y + z = 23) – (z + x = 16)
⇒ y = 7
Thus, x = 11, y = 7 and z = 5

Q5. Solve :
Hint: Inverting the equations:

Adding (1), (2) and (3), we get

Now, subtracting (1), (2) and (3) turn by turn from (4), we get x = 2, y = 4 and z = 6

Q6. Solve:
Hint:
From
⇒ 11(x + y – 3) = 2(3x + y) ⇒ 5x + 9y = 33    ...(1)
From
⇒ 11(x + 2y – 4) = 3(3x + y)
⇒ 2x + 9y = 44        ...(2)
Solving (1) and (2), we get x = 3 and y = 2

The document HOTS Questions: Pair of Linear Equations in Two Variables | Mathematics (Maths) Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## Mathematics (Maths) Class 10

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## FAQs on HOTS Questions: Pair of Linear Equations in Two Variables - Mathematics (Maths) Class 10

 1. What is a pair of linear equations in two variables?
Ans. A pair of linear equations in two variables is a set of two equations that involve two variables, typically represented as x and y, and the power of both variables is 1. The general form of a linear equation is ax + by = c, where a, b, and c are constants.
 2. How can we solve a pair of linear equations in two variables?
Ans. There are several methods to solve a pair of linear equations in two variables. Some common methods include the substitution method, elimination method, and graphical method. These methods involve manipulating the equations to eliminate one variable and solve for the other.
 3. Can a pair of linear equations in two variables have multiple solutions?
Ans. Yes, a pair of linear equations in two variables can have multiple solutions. If the two equations represent the same line, they have infinitely many solutions. If the two equations represent parallel lines, they have no solution. Otherwise, they will intersect at a single point, which is the solution.
 4. How can we determine if a given point is a solution to a pair of linear equations in two variables?
Ans. To determine if a given point is a solution to a pair of linear equations in two variables, substitute the values of the variables into both equations and check if the equations hold true. If both equations are satisfied, the point is a solution to the pair of equations.
 5. What real-life applications involve the use of a pair of linear equations in two variables?
Ans. A pair of linear equations in two variables is commonly used to model real-life situations. Some examples include solving problems related to cost and revenue, distance and time, speed and time, mixture problems, and optimization problems. These equations help in finding the unknown variables and making predictions or decisions based on the given conditions.

## Mathematics (Maths) Class 10

115 videos|478 docs|129 tests

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