Question

Which of the following is true and why?
 $ y = 2x + 4 $ has
A. A unique solution
B. only two solutions
C. infinitely many solutions

Answer 1

Hint: There are various methods to solve when two linear equations are given to us in two variables like substitution method, cross multiplication method, elimination method, matrix method and many more. In such a case, the equations given in the question can be solved using any one of the above mentioned methods easily. But in the given question, we are given a linear equation in two variables and we have to determine the number of solutions of the equation.

Complete step by step solution:
So, we have the linear equation in two variables $ y = 2x + 4 $ provided to us in the question itself. We have to find the number of solutions that the equation given to us possess.
Now, we know that a linear equation in two variables can be potted as a line on the two dimensional graph. So, a line can be plotted on the Cartesian plane that represents the graph of the equation $ y = 2x + 4 $ such that all the points lying on the line will satisfy the equation of the line given to us.
Now, we know that there is a line consisting of infinite points.
So, there are infinite solutions of the linear equation in two variables given to us, $ y = 2x + 4 $ . Therefore, option (c) is correct.
So, the correct answer is “Option C”.

Note: Every linear equation in two variables has infinite solutions. A pair of linear equations in two variables can have a unique solution, infinitely many solutions or no solution at all because the lines given to us can be the same line, or parallel lines as well.