Question

Use algebraic rules of equations to predict the solution type to the system of equations. Include all of your work for full credit.

Answer 1

The system has infinite solutions

Explanation:

For a system of two linear equations it is always true that if one equation is a linear combination of another, then the system will have infinite solutions.

Suppose we have the following system:

`ax + by = c\\dx + hy = f`

If there is a number n for which it is fulfilled that

`<a, b, c> = n * <d, h, f>`

Then the system has infinite solutions.

In this case the system is:

`x + 2y=10\\3x+6y =30`

Observe that:

`<1, 2, 10> = (1)/(3)* <3, 6, 30>`

Then
`n =(1)/(3)`

The system has infinite solutions