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.\\(\

$$\begin{cases}5x + 5y = 40\\\\2x - 10y = -44\\end{cases}$$

\\)\
show your work here\
\\(x =\\)\
\\(y =\\)\
check

Explanation:

Step1: Simplify the first equation

Divide the first equation \(5x + 5y = 40\) by 5, we get \(x + y = 8\), which can be rewritten as \(x = 8 - y\).

Step2: Substitute into the second equation

Substitute \(x = 8 - y\) into the second equation \(2x - 10y = -44\). So we have \(2(8 - y) - 10y = -44\).

Step3: Solve for y

Expand the left - hand side: \(16-2y - 10y=-44\). Combine like terms: \(16-12y=-44\). Subtract 16 from both sides: \(-12y=-44 - 16=-60\). Divide both sides by - 12: \(y=\frac{-60}{-12} = 5\).

Step4: Solve for x

Substitute \(y = 5\) into \(x = 8 - y\), we get \(x=8 - 5=3\).

Answer:

\(x = 3\), \(y = 5\)