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:

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