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find the solution of the system of equations. answer with the solution,…

Question

find the solution of the system of equations. answer with the solution, or with \all real numbers\ if there are infinite solutions, or with
o solution\ if there are no solutions.\

$$\begin{cases}-x + y = -4\\\\-7x + 5y = -14\\end{cases}$$

Explanation:

Step1: Solve first equation for y

From \(-x + y = -4\), add \(x\) to both sides: \(y = x - 4\)

Step2: Substitute y into second equation

Substitute \(y = x - 4\) into \(-7x + 5y = -14\):
\(-7x + 5(x - 4) = -14\)
Expand: \(-7x + 5x - 20 = -14\)
Combine like terms: \(-2x - 20 = -14\)
Add 20 to both sides: \(-2x = 6\)
Divide by \(-2\): \(x = -3\)

Step3: Find y using x = -3

Substitute \(x = -3\) into \(y = x - 4\):
\(y = -3 - 4 = -7\)

Answer:

\(x = -3\)
\(y = -7\)