Formation Of Linear Equations - Free MCQ Practice Test with solutions,

Let Geeta's age be G and Meeta's age be m. According to the given information:

• Geeta’s age is 3 years more than thrice Meeta's age.

This can be written as the equation:

G=3m+3

This is a first-degree equation that represents the relationship between Geeta's and Meeta's ages.

The equation (a) 1/x + 1/y = 4 is not a linear equation because the variables x and y are in the denominator.

A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form a x + b = 0, ax+b=0, ax+b=0 and are solved using basic algebraic operations

To express y = -5 in the form ax + by + c = 0:

• Start with y = -5.
• Subtract y from both sides to get 0x + y + 5 = 0.
• This matches option C: 0x + y + 5 = 0.

Option A, 2.4s + 3t = 7, is a linear equation because it has two variables sss and ttt, both with a power of 1, and follows the standard form of a linear equation ax + by + c = 0.
Option B contains t², which makes it non-linear. Option C has x², which violates the linear condition.
Option D includes 7/x, a rational term, which also disqualifies it as a linear equation.
Thus, the correct answer is Option A.

Correct Answer :- a

Explanation : Let number of girls in class = x

Boys = 2y - 5

Equation will be : x + 5 = 2y

The speed x of train A is twice the speed y of train B. This can be expressed as:

x = 2y

Answer: B) x = 2y

The cost of a pencil p is thrice the cost of a rubber r. The equation can be written as:
p = 3r
Answer: C) p = 3r

The given equation is: - (9/5) x = 1/2
To express it in the standard form of a linear equation in two variables ax + by + c = 0, we rearrange:
- 9/5x + 0.y - 1/2 = 0
Here:

• Coefficient of x is = - 9/5.
• Coefficient of y is 0 (no y-term is present).
• Coeficient term is -1/2.

Thus, the correct answer is Option D.

A linear equation with one variable consists of numbers or constants and multiplies of a variable. The standard form of such an equation is ax + b = 0, where a and b are constants and x is the variable.
Hence, 2x + 7 = 8  is a linear equation in one variable.

a = - 7/2 (coefficient of x), 
b = 5/4 (coefficient of y), 
c = 9 (constant term) .

(i) Not a solution: Substituting (11, 2), 3(11) + 2(2) = 33 + 4 = 37 (False).
(ii) Not a solution: Substituting (1, 4), 3(1) + 2(4) = 3 + 8 = 11 (False).
(iii) Is a solution: Substituting (0, 5), 3(0) + 2(5) = 0 + 10 = 10 (True).
(iv) Not a solution: Substituting (3, 1), 3(3) + 2(1) = 9 + 2 = 11 (False).

[√x]² + [√y]² = √2
Step 1: Simplify the terms
• [√x]² = x
• [√y]² = y
Thus, the equation becomes:
x + y = √2
Step 2: Check for linearity
• The variables  x and y both have degree 1.
• The constant √2 does not affect the linearity of the equation.
Conclusion:
This is a linear equation because it is of the form ax + by + c = 0, where a = 1, b = 1, and c = - √2.
Answer: The equation is linear.

The difference in costs of two articles is 200, and since the carpet is more costly than the durry. So the equation will be C - D = 200

Four times B's age: 4B
Exceeds A's age: - A
By twenty years: = 20
4B - A = 20