Question

Verify that (-4, 12) is the solution to the system. Show work to justify your answer.
$\left \{ {{2x+y=5} \atop {-5x-2y=-6}} \right.$

Answer 1

Focus on the first equation. The ordered pair (-4,12) means that x = -4 and y = 12. Keep in mind that x always comes first. Think alphabetical order.

What we do is simply replace every x with -4 and replace every y with 12. Let's see what happens

2x+y = 5
2*x+y = 5
2*(-4) + 12 = 5
-8 + 12 = 5
4 = 5

The last equation, 4 = 5, is FALSE. So because we have a false equation, it means that 2x+y = 5 is also false when (x,y) = (-4,12)

There is no way that (-4,12) is the solution to this system. It fails to satisfy the first equation. 

Answer 2

Equation 1)  2x + y = 5
Equation 2)  -5x - 2y = -6

We're trying to elminate (y) so that we could get (x) by itself, so to do so, we have to multiply ALL of equation 1 by 2, so that both equations have (2y) in them.

Equation 1)  2(2x + y = 5)

Equation 1)  4x+2y=10
 Equation 2) -5x-2y=-6

Add equations together.

-x=4

x=-4

Plug in (x) into equation 1.

2(-4)-2y=-6

Simplify.

-8-2y=-6

Add 8 to both sides.

-2y=2

Divide both sides by -2.

y=1

(-4, 1)

So, (-4, 12) is NOT the correct answer.

~Hope I helped!~