# Thread: Substitution (should be easy)

1. ## Substitution (should be easy)

Hello,
I have a problem where I have solved for Y and need to now solve for X. I am having trouble solving for X.

Y = (X/2) * (PX/PY)

X = (M/PX) - ((Py/PX) * Y))

Subsituting Y in to the equation gives:

X = (M/PX) - ((Py/PX) * ((X/2)*(PX/PY)))

I am having trouble working out the steps to break this down. I wrote the answer in my notes from class as:
X = (2M)/(3PX)

But I'm getting stuck on working out the steps.

Here is what I do:

Py/PX cancels out, so you are left with:

X = (M/PX) - (X/2)

Then I move X to one side:

(X/2) + X = (M/PX)

From here I can't remember what to do. I can't tell if I wrote the answer down wrong, or if I am just rusty. I am not sure how we get to: X = (2M)/(3PX)

Any help would be great. Thanks.

2. Originally Posted by lastlion
(X/2) + X = (M/PX)

From here I can't remember what to do.
Combine the terms on the left side. (Common denominator = 2)
\begin{aligned}
\frac{X}{2} + X &= \frac{M}{PX} \\
\frac{X}{2} + \frac{2X}{2} &= \frac{M}{PX} \\
\frac{3X}{2} &= \frac{M}{PX} \\
\frac{2}{3}\left(\frac{3X}{2}\right) &= \frac{2}{3}\left(\frac{M}{PX}\right) \\
X &= \frac{2M}{3PX}
\end{aligned}

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