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

Answer:

The system has infinite solutions

Step-by-step 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

$= n *$

Then the system has infinite solutions.

In this case the system is:

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

Observe that:

$= \frac{1}{3}*$

Then $n =\frac{1}{3}$

The system has infinite solutions