Question

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$$\begin{cases}5x - y = 1\\\\3x + y = 1\\end{cases}$$

Explanation:

Step1: Eliminate y by adding equations

Add the two equations \(5x - y = 1\) and \(3x + y = 1\) together.
\((5x - y)+(3x + y)=1 + 1\)
Simplify: \(8x=2\)

Step2: Solve for x

Divide both sides by 8: \(x=\frac{2}{8}=\frac{1}{4}\)

Step3: Substitute x into an equation

Substitute \(x = \frac{1}{4}\) into \(3x + y = 1\):
\(3\times\frac{1}{4}+y = 1\)
\(\frac{3}{4}+y = 1\)

Step4: Solve for y

Subtract \(\frac{3}{4}\) from both sides:
\(y = 1-\frac{3}{4}=\frac{1}{4}\)

Answer:

\(x=\frac{1}{4}, y=\frac{1}{4}\)