Question

Hey guys PLEASE HELP ME SO THIS ONE IS TRICKY AND COMPLEX I APPRECIATE IF SOMEONE REACHES OUT AND HELPS. 2X+Y=-14

Answer 1

You can certainly start out that way, but when you solve that equation for x, it's a little more complex than if you started with the other equation.  I usually start with the most simple equation first.  Let's take the first equation and solve for y... that will leave us without any fractions to deal with.

2x + y = -14
y = -14 - 2x

Now we have a y value and we can substitute it back into the other equation.  So we will replace y in the second equation with (-14 - 2x).
That will leave us with just the x as a variable and we can solve for x.

7x - 4y = -19
7x - 4(-14 - 2x) = -19      multiply the -4 through the parentheses
7x + 56 + 8x = -19          combine like terms
15x + 56 = -19                subtract 56 from each side
15x = -75                         divide each side by 15
x = -5

Now we have a value for x that we can substitute back into either of the original equations and then solve for y.  I usually go with the easier equation, but it doesn't matter.  Let's use the first one...

2x + y = -14
2(-5) + y = -14              multiply the 2 through the parentheses
-10 + y = -14                 add 10 to each side
y = -4

So your ordered pair is

(-5, -4)

That is where the 2 lines are equal to one another, so that's the point where they they intersect.

Note***  You can start these problems with either equation and solving for either x or y... it doesn't matter.  After you substitute the values into the other equation it will work out the same.