System solution

[Happymom]

Hi I need help with this problem

Determine if (-5,5) is a solution to the given system of equations

6x - 3y = -45
x + 3y = -15

Thanks

 

[Jameson]

Hi I need help with this problem

Determine if (-5,5) is a solution to the given system of equations

6x - 3y = -45
x + 3y = -15

Thanks

Hi Happymom! Welcome to MHB

To check this, you need to "plug in" -5 for x and 5 for y. Let's try the first one.

6x - 3y = 45

6(-5)-(3)(5) is the left hand side after we plug in x and y that they gave us. If we simpligy that we get -30-15=-45, which is good because in order to be a solution the left and right hand sides must be equal at the solution point.

Can you test the second equation?

 

[Happymom]

Hi Jameson

would x = -5 for x + 3y = -15

 

[Jameson]

Hi Jameson

would x = -5 for x + 3y = -15

Exactly! I forgot to mention the point (-5,5) is using the general form of (x,y). You'll see that often in graphing so it's worth memorizing. What do you get after plugging in x and y for the 2nd line?

 

[Happymom]

Jameson

I'm stumped! Can you show thanks

 

[Jameson]

Jameson

I'm stumped! Can you show thanks

Of course. The 2nd equation we are testing is x + 3y = -15. We are testing (-5,5) or x=-5 and y=5. Now we just replace any x's we see with -5 and any y's with 5.

That gives us -5+3(5) for the left hand side. That simplifies to -5+15=10. Uh oh! The right hand side of the original equation was -15 and we found the left hand side is 10 at this point so it's not a solution. Whenever a solution is valid you'll end up with something like 10 = 10 or -22 = -22 after testing the solution with your equation. Those are both true statements so that would mean the solution is valid.

In our problem just now, we found a result that wasn't true since 10 does not equal -15.