Help with Algebra 2 homework please?

Question

Check whether the ordered pair (5,6) is a solution of the system.

-2x+4y=-14
3x+y=21



Please explain in easy steps.
Thank you for your time!

Answer 1

All you need to do is plug the two into the equation.

5 is x, and 6 is y.

So lets plug it into the first equation first.

-10 + 24 = -14

Simplify.

14 = -14

Notice that they DO NOT equal each other. This means that it is not the solution to the system, but lets do the other one anyway.

15 + 6 = 21

Simplify.

21 = 21

This makes a true statement. According to this, it IS a solution to the system.

But, you know, one rotten apple in a barrel makes all the other ones go bad! (5, 6) isn't a solution to the entire system.

Answer 2

The ordered pair (5,6) just means x=5 and y=6. Simply plug in x=5 and y=6 in the 2 equations you provided. If they produce the answers you were expecting, then the ordered pair (5,6) is a solution.

I'll do the second one:
Plugging in x=5 and y=6 into 3x+y, you get:
3(5)+6=15+6=21, so it works for the second equation. If it also works for the first equation the pair is a solution.

Answer 3

-2x+4y=-14 -------1
3x+y=21----------2

Check this point pair (5,6)

plug into 1,
you have -2*5 + 4*6 = -14
-10 + 24 = -14
14 = -14, is that correct? no...
Usually you can stop here since it has proved the pair of point is not the solution is on the system. One point is sufficient to prove the whole system wrong, if in fact, it is wrong.
Just in case, check with the 2,
you plug in pair (5,6) into 3x+y=21

You get, 3*5 + 6 = 21
15 + 6 = 21
21 = 21 check!
So you may think well, it works on the 2, but since
-2x+4y=-14
3x+y=21
is working as a system, you have to have two equations work!
So the answer to your question is no.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In case you thought, uhhhh I want to solve the system,
Here is how:
-2x+4y=-14----------------1
3x+y=21--------------------2

solve for y in 2nd equation, 2.
y = 21 - 3x
plug into 1,
-2x + 4 (21 - 3x) = -14
-2x + 84 - 12x = -14
combine number part then combine x part.
-14x + 84 = -14
-14x = -14 - 84
-14x =- 98
x = 7
Now, plug back to y = 21 - 3x to solve for y,
y = 21 - 3x
y = 21 - 3*7 = 21 - 21 = 0

So you have a pair of (7, 0) as the real solution to your problem....


*still confused? write back

Answer 4

-2x + 4y = -14
-2(5) + 4(6) = -14
-10 + 24 = -14
14 does not = -14

3x + y = 21
3(5) + 6 = 21
15 + 6 = 21
21 = 21

Answer 5

Put x = 5 and y = 6 into the 1st equation, getting:
-2(5) +4(6) = -14
-10 +24 = -14
14 = -14 <--- FALSE
The ordered pair is not a solution

Answer 6

Just plug in 5 for x and 6 for y in both equations. If it comes up true in both, it's a solution for the system.

3(5)+6=21
15+6=21
21=21
This one is true. Now for the other equation:

-2(5)+4(6)=-14
-19+24=-14
5=-14
This isn't true. Even though it's a solution for the first equation, it isn't a solution for the system since it doesn't work here.