5x+4y = -14
3x+6y=6
can you explain how to do this

(-6, 4)

Step-by-step explanation:

There are two main ways you can solve a system of equations.  One is substitution, the other is elimination.

With substitution, you solve for one variable in one of the equations, then substitute that into the other equation.

With elimination, you add or subtract equations to eliminate a variable, then solve for the remaining variable.

Here, it is easier to use elimination.  Let's start by multiplying the first equation by 3 and the second equation by 5.

15x + 12y = -42

15x + 30y = 30

Now subtract the first equation from the second:

(15x + 30y) − (15x + 12y) = 30 − (-42)

18y = 72

y = 4

Now we can plug this into any of the original equations to find x.

5x + 4(4) = -14

5x + 16 = -14

5x = -30

x = -6

The solution is (-6, 4).  You can also show this graphically: desmos.com/calculator/mwdaztzhab