To solve the system of equations:
[tex]\[
\begin{cases}
y - 3x = 1 \\
y - 5x = -3
\end{cases}
\][/tex]
we'll proceed through a sequence of steps to find the solution.
### Step-by-Step Solution:
1. Rewrite the equations for clarity:
[tex]\[
\begin{cases}
y = 3x + 1 \quad \text{(Equation 1)} \\
y = 5x - 3 \quad \text{(Equation 2)}
\end{cases}
\][/tex]
2. Set the equations equal to each other since both are equal to [tex]\( y \)[/tex]:
[tex]\[
3x + 1 = 5x - 3
\][/tex]
3. Solve the equation for [tex]\( x \)[/tex]:
- Subtract [tex]\( 3x \)[/tex] from both sides:
[tex]\[
1 = 2x - 3
\][/tex]
- Add 3 to both sides:
[tex]\[
4 = 2x
\][/tex]
- Divide by 2:
[tex]\[
x = 2
\][/tex]
4. Substitute the value of [tex]\( x \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex]. We'll use Equation 1 for this purpose:
[tex]\[
y = 3(2) + 1
\][/tex]
[tex]\[
y = 6 + 1
\][/tex]
[tex]\[
y = 7
\][/tex]
So, the solution to the system of equations is:
[tex]\[
x = 2 \quad \text{and} \quad y = 7
\][/tex]
### Final Answer:
The correct answer is:
B. [tex]\( x = 2, y = 7 \)[/tex]
