Question

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$$\begin{cases} x + y = 7 \\\\ 9y - 2x = -25 \\end{cases}$$

Explanation:

Step1: Rearrange the first equation

From \(x + y = 7\), we can express \(x\) as \(x = 7 - y\).

Step2: Substitute \(x\) into the second equation

Substitute \(x = 7 - y\) into \(9y - 2x = -25\), we get:
\(9y - 2(7 - y) = -25\)

Step3: Simplify the equation

Expand the left - hand side: \(9y-14 + 2y=-25\)
Combine like terms: \(11y-14=-25\)
Add 14 to both sides: \(11y=-25 + 14=-11\)

Step4: Solve for \(y\)

Divide both sides by 11: \(y=\frac{-11}{11}=-1\)

Step5: Solve for \(x\)

Substitute \(y = - 1\) into \(x = 7 - y\), we have \(x=7-(-1)=7 + 1 = 8\)

Answer:

The solution of the system of equations is \(x = 8,y=-1\)