Question

Determine the type of solution from the following system of equations.Justify your reasoning.

y=3x+12
3y=9x+36

Are they One solution,No solution,or Infinite solution? How can you tell?

Answer 1

The system of equations has infinitely many solutions

Solution:

Given system of equations are:

y = 3x + 12 --------- eqn 1

3y = 9x + 36 ------ eqn 2

We have to find the type of solution

Let us first solve the system of equations by substitution method

Substitute eqn 1 into eqn 2

3(3x + 12) = 9x + 36

9x + 36 = 9x + 36

The equation has infinitely many solutions (in the variable x) if and only if both the overall coefficients of x on the two sides are equal, and the overall constants on the two sides are equal.

Here,

9x + 36 = 9x + 36

Thus the system has infinite solution