Question

Help please!!! If 2x + 5y = 21 and x + y = 3, then what is the value of x? It is your choice to use either substitution or elimination,

Answer 1

and can you please explain it to me!!

Answer 2

This is a system of equations. there are several methods for solving a system of equations.
I will show you the method called elimination.

Answer 3

In the elimination method, you always end up adding the equations in order to eliminate one valriable.

Answer 4

If you look at your equations, you have 2x and x. Added together, that is 3x. that is not eliminated.
Now if you look at the two y-terms you have 5y and y. Once again, when you add 5y and y, you get 6y, which means y is not eliminated.

Answer 5

You need to do something to one equations or to both equations so that when you add the equations together, one variable will add to zero.

Answer 6

The way you do that is to multiply one equation or both equations by a number or numbers. You choose the number or numbers carefully in a way that ensures one variable will be eliminated when the equations are added together.

Answer 7

what is happening? is it a lag?

Answer 8

2x+5y=21 2x+5y =21 2*( 3-y) +5y =21 6-2y+5y=21 => 6+3y=21
x+y=3 => x=3-y x=3-y x=3-y => x=3-y

3y=21-6 => 3y=15 => y= 15/3 => y=5 => y=5
x=3-y =>x=3-y => x=3-y => x=3-5 => x= -2

As you can see you just substitute at the top the x for 3-y, so you get an equation with one unknown variable, and when you get the value of Y, you put it at the other equation , to get the value of x.
I hope this makes sense :)

Answer 9

okay i get half of it but the question?

Answer 10

Well, the value of x appears to be -2. If thats what you're looking for.

Answer 11

2x + 5y = 21
x + y = 3

Since you are solving only for x, we need to eliminate y.
If you multiply the second equation by -5, the y term of the second equation will become -5y. Then when you add that -5y term to the 5y of the first equation, you eliminate the y terms leaving only x.

2x + 5y = 21 --- (just copy the equation) ----> 2x + 5y = 21
x + y = 3 --- (multiply entire eq. by -5) ---> -5x - 5y = -15

(add) --------------
-3x = 6

Once you add the equations, you get

-3x = 6. This equation can now be easily solved for x.

Divide both sides by -3:

x = -2

Answer 12

ohhhh