Question

-10x-6y=0 -4x -6y=54 find the solution of this system of equations

Answer 1

You can see that the term $-6y$ appears in both equations. In this cases, we can leverage this peculiarity and subtract the two equations to get rid of the repeated term. So, if we subtract the first equation from the second, we have

$(-4x -6y) - (-10x-6y) = 54-0 \iff 6x = 54 \iff x = 9$

Now that we know the value of $x$, we can substitute in any of the equation to deduce the value of $y$: if we use the first equation, for example, we have

$-10x-6y=0 \iff -10\cdot 9 - 6y = 0 \iff -90-6y=0 \iff 6y = -90 \iff y = -15$