Question

Solve the equation for y.

5x – 7y = 10

Answer 1

@whpalmer4

Answer 2

@tkhunny

Answer 3

@mathmale

Answer 4

Show you work rather than tagging the world.

Answer 5

@blake57roger

to solve for some variable, you need to rearrange the equation so that the variable is alone on one side of the equals sign, and everything else is on the other side.

to do this, you can do just about anything you want, with the catch that you must do it to both sides of the equation.

for example:

\[3x+4y=15+y\]to solve this for \(y\), let us first get everything containing \(y\) on one side, and remove everything that does not contain \(y\) from that side. We have a couple of options, but let's start by subtracting \(y\) from both sides, which will give us this:

\[3x+4y-y = 15+y-y\]which simplifies to:\[3x+3y=15\]

now we have everything containing \(y\) on the left side. Let us get rid of everything else from that side. We can do that by subtracting \(3x\) from both sides:

\[3x+3y-3x=15-3x\]which simplifies to:\[3y=15-3x\]
We are within range of our goal. we just need to get rid of that pesky \(3\) in front of \(y\) and we will be done. We can do that by dividing both sides by \(3\):
\[\frac{3y}3=\frac{15}3-\frac{3x}3\]which simplifies to:\[y=5-x\]

That should show you how to solve your particular problem.