Someone please tell me I’m not the only one who doesn’t know how to solve this
You probably do, the phrase “equation with multiple solutions” is just phrased poorly if you haven’t seen that wording. Basically you need to make both sides of the equation equal each other so that any y-value would solve it.
It’s not even algebra really, just simplifying fractions.
I struggled with it for a while. It’s worded really weird.
Use “x” to represent the input box:
½ y + ¼ = ¹⁄₁₂ (3 + xy)
Distribute the ¹⁄₁₂ on the right:
½ y + ¼ = ¹⁄₁₂ * 3 + ¹⁄₁₂ * xy
Simplify the right hand side:
½ y + ¼ = ¼ + ¹⁄₁₂ xy
Subtract ¼ from both sides:
½ y = ¹⁄₁₂ xy
Divide both sides by y:
½ = ¹⁄₁₂ x
Multiply both sides by 12:
½ * 12 = ¹⁄₁₂ x * 12
Multiply the fractions together and simplify
x = 6
Hell, I wouldn’t even do that. Simplfy the fractions by finding a common denominator, which everything being divisible by 12 makes 12 the easy common denominator. So you have (6y+3)/12=(1/12)(3+xy). Multiply 12 through to get rid of all those fractions, leaving 6y+3=3+xy. Now you can get rid of three from both sides, leaving 6y=xy then just divide by y leaving x=6.
Your formatting is better though lol.
The common denominator is simpler, but I was hoping to write it out in a way that someone who didn’t understand how to do it would have an easy time following at every step. Like how you might do it if you didn’t see the shortcut and were just playing with it to see what you could find. I would normally do most of these steps implicitly in my head in between steps. But that can be hard to follow.
