Question 1204913
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Answers: <font color=red size=4>k = 6 and m = 4</font>


Explanation


Add 3a to both sides and add mb to both sides to get the 'a's and 'b's together
6a + 2b = k - 3a - mb
6a + 3a + 2b + mb = k
9a + (2 + m)b = k


This system
{{{system(3a + 2b = 2,6a + 2b = k - 3a - mb)}}}
is equivalent to this system
{{{system(3a + 2b = 2,9a + (2 + m)b = k)}}}
The jump from 3a to 9a is "times 3", so let's triple everything in the 1st equation
3a + 2b = 2 triples to 9a + 6b = 6


We now have this equivalent system
{{{system(9a + 6b = 6,9a + (2 + m)b = k)}}}


To have the coefficients for b to match up, we must have {{{6 = 2+m}}} be the case. That solves to {{{m = 4}}}
We must have {{{k = 6}}} so the right hand sides match up.


In short: <font color=red>k = 6 and m = 4</font>
Let's plug those into the original 2nd equation
6a + 2b = k - 3a - m*b
6a + 2b = 6 - 3a - 4b
6a + 2b + 3a + 4b = 6
9a + 6b = 6
3(3a + 2b) = 6
3a + 2b = 6/3
3a + 2b = 2
We arrive at the 1st original equation. 
It proves that equation2 is the same as equation1 when k = 6 and m = 4.
The answers are confirmed.


Another way to confirm the answers is to graph the equations 3x+2y = 2 and 6x+2y = k - 3x - m*y
I have replaced 'a' with x, and b with y.
After inputting those equations into Desmos or GeoGebra, set the parameters k = 6 and m = 4 to notice one line overlaps the other perfectly.
Link to interactive Desmos graph
<a href="https://www.desmos.com/calculator/rzgnjxxyfc">https://www.desmos.com/calculator/rzgnjxxyfc</a>
Click the button for one of the equations to turn the line on/off. Do this repeatedly. The line will blink different colors to show the overlap. 
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