Question

Determine if the following systems of equations have one, none or infinitely many solutions.

x+3y=5
4x+12y=20

A. Infinite number of solutions

B. No Solution

C. One solution

D. No answer text provided.

Answer 1

Answer: A. Infinite number of solutions

Explanation:

The given system of equations is expressed as

x + 3y = 5- - - - - - - - - - - - - -1

4x + 12y = 20- - - - - - - - - - - 2

We would apply the method of substitution. From equation 1, we would make x the subject by subtracting 3y from the left hand side and the right hand side of the equation. It becomes

x + 3y - 3y = 5 - 3y

x = 5 - 3y

Substituting x = 5 - 3y into equation 2, it becomes

4(5 - 3y) + 12y = 20

20 - 12y + 12y = 20

20 = 20

Therefore, the system of equations has an infinite number of solutions because as many values of x and y that satisfy the first equation, they would also satisfy the second equation.