Not sure what this is: 2y - x = 984, y - x = 350

[MeninaLaBela]

I got a packet to help me with my algebra, but I forgot how to do this:

2y - x = 984
y - x = 350

Any help is appreciated. Thank you!

 

[wantedcriminal03]

Hello.

What you have is a simultaneous equation:

you have to take the second equation from the first one to leave one variable which equals a known value as follows:

$\displaystyle 2y-x=984$ -
$\displaystyle y-x=350$

2y-y=y
-x-(-x) =-x+x=0
and 984-350 = 634

so you get

$\displaystyle y=634$

You then substitute y back into either equation, (y-x=350 is easier).

So 634-x=350
284-x=0
x=284

Depending on the eqations involved in the simultaneous equations you may also need to add them or multiply one equation by a certain number so they cancel out.

 

[soroban]

Hello, MeninaLaBela!

Here's an alternate method . . .

\(\displaystyle \begin{array}{cc}2y\,-\,x\:=\:984 \\ y\,-\,x\:=\:350\end{rray}\)

Solve the first equation for $\displaystyle x:\;\;2y\,-\,x\:=\:984\;\;\Rightarrow\;\;x\:=\:2y\,-\,984\;$ [1]

Solve the second equation for $\displaystyle x:\;\;y\,-\,x\:=\:350\;\;\Rightarrow\;\;x\:=\:y\,-\,350\;$ [2]

Equate [1] and [2]: $\displaystyle \,2y\,-\,984\:=\:y\,-\,350$

And solve: $\displaystyle \,2y\,-\,y\:=\:-350\,+\,984\;\;\Rightarrow\;\;$y = 634

Substitute into [2]: $\displaystyle \,x\:=\:634\,-\,350\;\;\Rightarrow\;\;$x = 284