Understanding Substitution Problem

Question

Instructions: Solve by either elimination or substitution. If the system is inconsistent or dependent, say so.

$y=4.9x$ and $-3.2y=x$

How would I go about solving this. So far I have:

$y=4.9(-3.2y)$

$y=-15.68y $ -then subtract the y on the right hand side...

$0=-15.68$

Not a true statement, therefore inconsistent. However, the answer is $x=0$ and $y=0$

What am I doing wrong?

Answer 1

First equation implies $y = 4.9x$ and second implies $x = -3.2y$, so putting it all together, you have $$ y = 4.9x = 4.9(-3.2)y $$ which only has a solution at $y=0$, which implies $x=0$ as well.

Answer 2

The only solution to $y=-15.68y$ is $y=0$.

Your mistake is when you subtract $y$ from both sides you should get $y-y=-15.68y-y \implies 0=-16.68y$, and divide both sides by $-16.68$ to get $y=0$.

Answer 3

From $y=-15.68y$ when you subtract $y$ from both sides you should get $0=-16.68y.\ $ Then it should be clear that $y=0$ is a solution.