Linear equation in 2 variables

Q. If we multiply or divide both sides of a linear equation with a non- zero number, then the solution of the linear equation

1. remains the same
2. only changes in case of division
3. Only changes in case of multiplication
4. Changes

Q.

How do you find the minimum value of a linear equation $?$

Q.

Finding the value of a variable in a linear equation that_____ the equation is called a ______ of the equation.

Q.

Two variables which are directly proportional to each other always give a linear relationship.

1. True
2. False

Q.

A linear equation in two variables

1. Has no solution

2. Has one solution

3. Has two solutions

4. Has infinitely many solutions

Q.

How many linear equations are satisfied by $x=3$ and $y=-2$?

1. Only one

2. Two

3. Three

4. Infinitely many

Q.

A two digit number $xy$ can be represented as

1. $x+y$
2. $10x+y$
3. $x^y$

4. $2x+y$

Q. x = 5, y = 2 is the solution of the linear equation:

1. 5x+y=7
2. x+2y=7
3. x+y=7
4. 5x+2y=7

Q.

If a, b and c are positive integers and (a - b)c = 0, which statement must be true?

1. b > a

2. b = c

3. a = b

4. a < c

Q.

Which of the following represents a linear equation in two variables?

1. 
   where, x is a variable and a, b are real numbers

2. 
   where, a, b, c are real numbers and xy ≠ 0, and x, y are variables

3. =
   where, a, b, c are real numbers and + ≠ 0

4. 
   where, a, b, c are the variables and x, y are real numbers

Q. The price of 1 kg oranges is thrice the price of 1 kg apples. Which of the following linear equation represents the given statement ?
(Assume the the price of 1 kg oranges to be x and of 1 kg apples to be y)

1. x - 3y = 0
2. 2x + 1 = y
3. 3x - y = 0
4. x + 3y = 0

Q.

Which equation is written in standard form?

1. 2x = 3y - 7

2. 2x + 3y = 6

3. 4x + 9y - 6 = 0

4. y = 2x + 3

Q. Match the two columns
$\begin{array}{cc}\text{Equations}& \text{Solutions}\\ \left(A\right)2x+y=7& \left(p\right)(0,9)\\ \left(B\right)x-2y=4& \left(q\right)(1,5)\\ \left(C\right)x-4y=0& \left(r\right)(0,0)\\ \left(D\right)px+y=9& \left(s\right)(4,0)\end{array}$

1. $\left(A\right)\to s;\left(B\right)\to p;\left(C\right)\to q;\left(D\right)\to r$
2. $\left(A\right)\to q;\left(B\right)\to r;\left(C\right)\to p;\left(D\right)\to s$
3. $\left(A\right)\to p;\left(B\right)\to q;\left(C\right)\to s;\left(D\right)\to r$
4. $\left(A\right)\to q;\left(B\right)\to s;\left(C\right)\to r,\left(D\right)\to p$

Q. Vihan spent ₹ 132 to buy movie tickets for 20 children and 4 adults. Each adult ticket costs ₹ 3 more than the child ticket. If A is the price of an adult ticket and S is the price of a child ticket, which system of equations could be used to find the price of each adult and child ticket?

1. $\left\{\begin{array}{c}A=S+3\\ 4A+20S=132\end{array}\right\}$
2. $\left\{\begin{array}{c}A=S+3\\ 20A+4S=132\end{array}\right\}$
3. $\left\{\begin{array}{c}S=A+3\\ 20A+4S=132\end{array}\right\}$
4. $\left\{\begin{array}{c}S=A+3\\ 4A+20S=132\end{array}\right\}$

Q.

A two digit number is such that the sum of itself and the number obtained when its digits are reversed is 55. Using the given data, write the simplest equation possible in two variables.

1. $x+y=5$

2. $x+\frac{1}{x}=55$

3. $x+5=y$

4. $2x+2y=55$

Q.

What do we call a system of equations that don't have a solution?

1. Inconsistent

2. Consistent

3. Independent

4. Coincident

Q. The equation $ax+by+c=0$ completely describes a linear equation in two variables where $a$, $b$, and $c$ are real numbers.

1. True
2. False