Correct Answer - Option 3 : It has infinite number of solutions
Explanation:
The given equation is y - 2 = 3x + 6 i.e., y = 3x + 8 which is a linear equation in two variables.
On putting, x = 0 in this equation, we get
y = 3(0) + 8 = 0
So, (0, 0) is the solution of the equation.
Similarly, if we put x = 1, we get
y = 3(1) + 8 = 11
So, (1, 11) is also the solution of the equation.
Similarly, if we put x = 2, we get
y = 3(2) + 8 = 6 + 8 = 14
So, (2, 14) is also the solution of the equation.
Clearly, for different values of x, we get various values for y. Thus, any value substituted for x in the given equation will constitute another solution for the given equation.
And there is no end to different solutions of linear equations in two variables.
Therefore, a linear equation in two variables has infinitely many equations.
Hence, y - 2 = 3x + 6 has infinite number of solutions.
