Question

A linear equation in two variables has how many solutions?
A) One
B) Two
C) Infinite
D) Not possible

Answer 1

Hint: In this question, we have been asked the number of solutions that a linear equation in two variables has. Read about what is a linear equation and their further types. Then, answer the question by choosing the perfect option.

Complete step-by-step solution:
We have been asked the number of solutions that a linear equation in two variables has. Let us read about equations and their types first.
What is an equation?
An equation is a statement, having a sign of equal $' = '$ between two mathematical expressions.
Example:
1) $2x + 4{x^2} = 12$
2) $3x + 4y = 9$
Moving towards linear equations. When the highest degree of the variables in the equation is 1, then the equation is known as linear equation. For example:
1) $3x + 4y = 9$
2) $8x - 72 = 0$
3) $6x + 5y = 7z$
Similarly, when the highest degree of the variables in the equation is 2, then the equation is known as quadratic equation. And when the highest degree of the variables in the equation is 3, then the equation is known as the cubic equation. Few examples are:
1) $2x + 4{x^2} = 12$ and $5x + 7{y^2} = 34$ are quadratic equations.
2) $x + 9{y^3} = 78$ and $7{x^3} = 343$ are cubic equations.
If a linear equation has one variable, it is called linear equation in one variable and if it has two variables, then it is called linear equation in two variables and so on.
Moving towards the question, if we draw a graph of a linear equation in two variables, it will be a straight line. Every point of the line represents a solution. Hence, there are infinitely many solutions.

$\therefore $ The option C) infinite is the correct answer.

Note: See the graph. I have plotted points for the equation $3x + 4y = 9$. There are an infinite number of points on the line and each point on the line represents a solution.