If \(6x-10y=10\) and \(\frac{x}{x+y}=\frac{5}{7}\), then \((x-y)\) is equal to:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3
The ratio equation gives \(x\) in terms of \(y\); putting that into the linear equation leaves one unknown.
From the ratio:
\(\displaystyle \frac{x}{x+y}=\frac{5}{7}\) gives \(7x=5x+5y\)
\(2x=5y\), so \(\displaystyle x=\frac{5y}{2}\) (1)
Putting (1) into \(6x-10y=10\):
\(15y-10y=10\)
\(5y=10\), so \(y=2\)
From (1), \(x=5\)
So \(x-y=5-2=3\).