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.\

$$\begin{cases}-2x - 2y = 8\\\\-14x + 5y = 56\\end{cases}$$

Explanation:

Step1: Simplify the first equation

Divide the first equation \(-2x - 2y = 8\) by \(-2\) to simplify. We get \(x + y = -4\), which can be rewritten as \(x = -4 - y\).

Step2: Substitute into the second equation

Substitute \(x = -4 - y\) into the second equation \(-14x + 5y = 56\). So we have \(-14(-4 - y) + 5y = 56\).
Expand the left - hand side: \(56+14y + 5y=56\).
Combine like terms: \(56 + 19y=56\).
Subtract 56 from both sides: \(19y=56 - 56=0\), so \(y = 0\).

Step3: Find the value of x

Substitute \(y = 0\) into \(x=-4 - y\). Then \(x=-4-0=-4\).

Answer:

\(x=-4\), \(y = 0\)