To solve the system of equations given by
[tex]\[ 2r + 2s = 50 \][/tex]
[tex]\[ 2r - s = 17 \][/tex]
we'll determine the values of \( r \) and \( s \) by following these steps:
1. First, simplify the system of equations if possible:
[tex]\[ \begin{aligned}
2r + 2s &= 50 \ \ \ \ \ \text{(Equation 1)} \\
2r - s &= 17 \ \ \ \ \ \text{(Equation 2)}
\end{aligned} \][/tex]
2. Solve Equation 2 for one of the variables:
Let's solve Equation 2 for \( s \):
[tex]\[ \begin{aligned}
2r - s &= 17 \\
-s &= 17 - 2r \\
s &= 2r - 17 \ \ \ \ \ \text{(Equation 3)} \\
\end{aligned} \][/tex]
3. Substitute Equation 3 into Equation 1:
Substitute \( s = 2r - 17 \) into Equation 1:
[tex]\[ \begin{aligned}
2r + 2(2r - 17) &= 50 \\
2r + 4r - 34 &= 50 \\
6r - 34 &= 50 \\
6r &= 50 + 34 \\
6r &= 84 \\
r &= \frac{84}{6} \\
r &= 14
\end{aligned} \][/tex]
4. Substitute \( r = 14 \) back into Equation 3 to find \( s \):
[tex]\[ \begin{aligned}
s &= 2r - 17 \\
s &= 2(14) - 17 \\
s &= 28 - 17 \\
s &= 11
\end{aligned} \][/tex]
Therefore, the solution to the system of equations is \( r = 14 \) and \( s = 11 \).
So, the correct answer is:
A. [tex]\( r = 14, s = 11 \)[/tex]
