Linear Equation in 2 Variables

Q.

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

1. a = b

2. b > a

3. a < c

4. b = c

Q.

There are two numbers. If 2490 is subtracted from one number then we get the other number. The algebraic expression depicting this information is:

1. a + b = 2490

2. a - b = 2490

3. a + b + 2490 = 0

4. a – b + 2490 = 0

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

Q.

Which equation is written in standard form?

1. 2x = 3y - 7

2. y = 2x + 3

3. 2x + 3y = 6

4. 4x + 9y - 6 = 0

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.

A two digit number $xy$ can be represented as

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

4. $2x+y$

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.

I have a certain number of chocolates. My friend has 4 more than twice the number of chocolates I have. Which of the following equations depicts the relation between the number of chocolates with me and my friend?
($x$ - no. of chocolates I have, and $y$ - no. of chocolates my friend has)

1. $y=2x+4$

2. $4y=x+2$

3. $x+2y=4$

4. $2y=x+4$

Q.

A linear equation in two variables has _____________

1. two solutions

2. four solutions

3. infinite solutions

4. one solution

Q. The standard form of a linear equation in two variables x and y, whose respective coefficients are 2 and -3 and has the constant as 4 is ____.

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