Fuxufzyg ugchcivgixigcigciigcigficyi
Answer:
7/25
Step-by-step explanation:
The fraction is not reduced to lowest terms. We can reduce this fraction to lowest terms by dividing both the numerator and denominator by 4. 4 is the Greatest Common Divisor (GCD) or Greatest Common Factor (GCF) of the numbers 28 and 100.
first off, let's split the triplet into two equations, then from there on we'll do substitution.
![\cfrac{y}{x-z}=\cfrac{x}{y}=\cfrac{x+y}{z}\implies \begin{cases} \cfrac{y}{x-z}=\cfrac{x}{y}\\[2em] \cfrac{x}{y}=\cfrac{x+y}{z} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{\cfrac{y}{x-z}=\cfrac{x}{y}\implies }y^2=\underline{x^2-xz} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 2nd equation}}{\cfrac{x}{y}=\cfrac{x+y}{z}\implies }xz=xy+y^2\implies \stackrel{\textit{substituting for }y^2}{xz=xy+(\underline{x^2-xz})}](https://tex.z-dn.net/?f=%5Ccfrac%7By%7D%7Bx-z%7D%3D%5Ccfrac%7Bx%7D%7By%7D%3D%5Ccfrac%7Bx%2By%7D%7Bz%7D%5Cimplies%20%5Cbegin%7Bcases%7D%20%5Ccfrac%7By%7D%7Bx-z%7D%3D%5Ccfrac%7Bx%7D%7By%7D%5C%5C%5B2em%5D%20%5Ccfrac%7Bx%7D%7By%7D%3D%5Ccfrac%7Bx%2By%7D%7Bz%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Busing%20the%201st%20equation%7D%7D%7B%5Ccfrac%7By%7D%7Bx-z%7D%3D%5Ccfrac%7Bx%7D%7By%7D%5Cimplies%20%7Dy%5E2%3D%5Cunderline%7Bx%5E2-xz%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Busing%20the%202nd%20equation%7D%7D%7B%5Ccfrac%7Bx%7D%7By%7D%3D%5Ccfrac%7Bx%2By%7D%7Bz%7D%5Cimplies%20%7Dxz%3Dxy%2By%5E2%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bsubstituting%20for%20%7Dy%5E2%7D%7Bxz%3Dxy%2B%28%5Cunderline%7Bx%5E2-xz%7D%29%7D)
![2xz=xy+x^2\implies 2xz=x(y+x)\implies \cfrac{2xz}{x}=y+x \\\\\\ 2z=y+x\implies 2=\cfrac{y+x}{z}\implies 2=\cfrac{x+y}{z} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{}{ \begin{cases} \cfrac{y}{x-z}=\cfrac{x}{y}\\[2em] \cfrac{x}{y}=\cfrac{x+y}{z} \end{cases}}\implies \begin{cases} \cfrac{y}{x-z}=\cfrac{x}{y}\\[2em] \cfrac{x}{y}=2 \end{cases}\implies \begin{cases} \cfrac{y}{x-z}=2\\[2em] \cfrac{x}{y}=2 \end{cases}](https://tex.z-dn.net/?f=2xz%3Dxy%2Bx%5E2%5Cimplies%202xz%3Dx%28y%2Bx%29%5Cimplies%20%5Ccfrac%7B2xz%7D%7Bx%7D%3Dy%2Bx%20%5C%5C%5C%5C%5C%5C%202z%3Dy%2Bx%5Cimplies%202%3D%5Ccfrac%7By%2Bx%7D%7Bz%7D%5Cimplies%202%3D%5Ccfrac%7Bx%2By%7D%7Bz%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%7D%7B%20%5Cbegin%7Bcases%7D%20%5Ccfrac%7By%7D%7Bx-z%7D%3D%5Ccfrac%7Bx%7D%7By%7D%5C%5C%5B2em%5D%20%5Ccfrac%7Bx%7D%7By%7D%3D%5Ccfrac%7Bx%2By%7D%7Bz%7D%20%5Cend%7Bcases%7D%7D%5Cimplies%20%5Cbegin%7Bcases%7D%20%5Ccfrac%7By%7D%7Bx-z%7D%3D%5Ccfrac%7Bx%7D%7By%7D%5C%5C%5B2em%5D%20%5Ccfrac%7Bx%7D%7By%7D%3D2%20%5Cend%7Bcases%7D%5Cimplies%20%5Cbegin%7Bcases%7D%20%5Ccfrac%7By%7D%7Bx-z%7D%3D2%5C%5C%5B2em%5D%20%5Ccfrac%7Bx%7D%7By%7D%3D2%20%5Cend%7Bcases%7D)
that of course, is only true if x + y, or our numerator doesn't turn into 0, if it does then our fraction becomes 0 and our equation goes south. Keeping in mind that x,y and z are numeric values that correlate like so.
In <em>slope-intercept form</em>, the <em>y</em> is isolated or
by itself on the left side of the equation.
Start by subtracting 2x from both sides and we have -3y = -2x.
Then we divide both sides by -3 to get <em>y = 2/3x</em>.
Work is provided in the image below.
Answer:
Step-by-step explanation:
