Question

Part 1: Solve the system using linear combination or substitution. Show all work.

{x+2y=4
{3x+6y=18
Part 2: Classify the system as consistent independent, inconsistent, or coincident.

Answer 1

Sorry for the sloppy handwriting!

Explanation:

Answer 2

Part 1:

We can solve the first equation in terms of x or y, here we solve for x in terms of y:

x+2y=4

x=4-2y

We can then substitute this expression for x into the second equation:

3x+6y=18

6(4-2y)+6y=18

12-6y+6y=18

12=18

This equation is not true for any value of y. Therefore, the system is inconsistent and has no solution.

Part 2:

Since the system has no solution, it si classified as inconsistent.