Transcript text: (1) $\quad \begin{aligned} 3 x-2 y & =6 \\ 5 x-5 y & =10\end{aligned}$
Solution
Solution Steps
To solve the system of linear equations, we can use the method of substitution or elimination. Here, we'll use the elimination method to eliminate one of the variables by making the coefficients of either \(x\) or \(y\) the same in both equations. Then, we'll solve for the remaining variable and substitute back to find the other variable.
Step 1: Set Up the Equations
We start with the system of equations:
\[
\begin{aligned}
& \quad 3x - 2y = 6 \\
& \quad 5x - 5y = 10
\end{aligned}
\]
Step 2: Solve for Variables
By solving the system, we find:
\[
x = 2, \quad y = 0
\]
Final Answer
The solution to the system of equations is:
\[
\boxed{x = 2, \, y = 0}
\]