Balancing Scales - Elimination

https://brilliant.org/practice/elimination/?p=7 Hello, I am making the Balancing Scales Course and now I am not sure wether all operations I did were valid:

R - Rectangle; T - Triangle

3R + 2 T = 5

2R + 5T = -4

The official solution is to multiply the top row and triple the second

6R + 4T = 10

6R + 15T = -12

so 11T = -22 divide this by 11 and T = -2

But trying to solve this I tried to add both of the left and both of the right sides together 5R + 7T = 5 - 4 = 1 but if you would divide the third line (6R + 4T = 10) by 10:

0.6R + 0.4T = 1

Are both of those valid? Does 0.6R + 0.4T = 5R + 7T? I just never been that good in math but now I am trying to get into it. I hope someone can helpt me

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$