Question

Which one of the following options is true, and why? y = 3x + 5 has
(i) a unique solution
(ii) only two solutions
(iii) infinitely many solutions

Answer 1

Answer:

• y = 3x + 5 is a linear equation in two variables and it has infinite possible solutions.
• As for every value of x, there will be a value of y satisfying the above equation and vice-versa.
• Hence, the correct answer is (iii).

Answer 2

y = 3x + 5 has infinitely many solutions. (Option iii)

• In this equation, any value of x will give a different value of y.
• For example- if x=1, y=3(1)+5=8. If x=0, y=3(0)+5=5 and so on.
• The value of x can be any real number and it will give another real value of y.
• So, the given equation will have infinite solutions.
• Since there is no limit to the values obtained of x and y, iii is the correct option.