Explanation: Here we are multiplying the second equation by a number and then we will add both equations and our intention is to eliminate the variable "x" of the result of the sum.
Step 1: First let's get the result of the multiplication of the first equation by 3 as follows
[tex]\begin{gathered} 4x-3x=\mleft(6\mright) \\ \mleft(4x-3x\mright)\mleft(3\mright)=\mleft(6\mright)\mleft(3\mright) \\ 12x-9x=18 \end{gathered}[/tex]
Step 2: As we can see we have a 12x on the first equation (after multiplying by 3) and a 6x on the second one so we just need to find a number that multiplies 6x that gives us -12x once 12x + (-12x) = 0x.
We can see that 6x * (-2) = -12x
So the have
[tex]\begin{gathered} 6x+y=10 \\ (6x+y)(-2)=10(-2) \\ -12x-2y=-20 \end{gathered}[/tex]
Above we have our second equation after multiplying it by -2
Step 3: Now we can try to sum both equations to see if it works as expected
see the calculation below
Final answer: As we can see above our assumption was right so the final answer is -2
