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.\\(\

$$\begin{cases}5x - 3y = 25\\\\3x + 9y = 15\\end{cases}$$

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

Explanation:

Step1: Eliminate y by multiplying first equation

Multiply the first equation \(5x - 3y = 25\) by 3: \(15x - 9y = 75\)

Step2: Add the two equations

Add the new first equation \(15x - 9y = 75\) and the second equation \(3x + 9y = 15\):
\((15x + 3x)+(-9y + 9y)=75 + 15\)
\(18x = 90\)

Step3: Solve for x

Divide both sides by 18: \(x=\frac{90}{18}=5\)

Step4: Substitute x into second equation

Substitute \(x = 5\) into \(3x + 9y = 15\):
\(3(5)+9y = 15\)
\(15 + 9y = 15\)

Step5: Solve for y

Subtract 15 from both sides: \(9y = 0\)
Divide by 9: \(y = 0\)

Answer:

\(x = 5\), \(y = 0\)