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.\

$$\begin{cases}7x + 7y = 56\\\\42x + 4y = 146\\end{cases}$$

\
show your work here\
x =\
y =

Explanation:

Step1: Simplify first equation

Divide the first equation \(7x + 7y = 56\) by 7:
\(\frac{7x}{7}+\frac{7y}{7}=\frac{56}{7}\)
Simplifies to: \(x + y = 8\), so \(y = 8 - x\).

Step2: Substitute \(y\) into second equation

Substitute \(y = 8 - x\) into \(42x + 4y = 146\):
\(42x + 4(8 - x) = 146\)
Expand: \(42x + 32 - 4x = 146\)
Combine like terms: \(38x + 32 = 146\)

Step3: Solve for \(x\)

Subtract 32 from both sides: \(38x = 146 - 32 = 114\)
Divide by 38: \(x=\frac{114}{38}=3\)

Step4: Solve for \(y\)

Substitute \(x = 3\) into \(y = 8 - x\):
\(y = 8 - 3 = 5\)

Answer:

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