Let's solve the given system of equations step-by-step to determine the current ages of Sam and Harry:
The system of equations is:
[tex]\[
\begin{cases}
x = 5y \\
x = 10 + 3y
\end{cases}
\][/tex]
1. Equate the equations:
Since both equations equal [tex]\( x \)[/tex], we can set the right-hand sides of these equations equal to each other:
[tex]\[
5y = 10 + 3y
\][/tex]
2. Isolate the variable [tex]\( y \)[/tex]:
Subtract [tex]\( 3y \)[/tex] from both sides of the equation to isolate [tex]\( y \)[/tex]:
[tex]\[
5y - 3y = 10
\][/tex]
[tex]\[
2y = 10
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
Divide both sides by 2 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = 5
\][/tex]
So, Harry's age ([tex]\( y \)[/tex]) is 5 years old.
4. Substitute [tex]\( y \)[/tex] back into the first equation to find [tex]\( x \)[/tex]:
Using the first equation [tex]\( x = 5y \)[/tex]:
[tex]\[
x = 5 \times 5
\][/tex]
[tex]\[
x = 25
\][/tex]
So, Sam's age ([tex]\( x \)[/tex]) is 25 years old.
Therefore, the correct ages are:
- Sam is 25 years old.
- Harry is 5 years old.
So, the correct answer is:
Sam is 25 years old and Harry is 5 years old.
