To solve the given system of equations, we need to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations simultaneously. The system of equations is:
[tex]\[
\begin{array}{l}
y = 2x \\
y = x + 5
\end{array}
\][/tex]
Step-by-step solution:
1. Set the equations equal to each other since both are equal to [tex]\( y \)[/tex]:
[tex]\[
2x = x + 5
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
- Subtract [tex]\( x \)[/tex] from both sides of the equation:
[tex]\[
2x - x = 5
\][/tex]
- Simplify the equation:
[tex]\[
x = 5
\][/tex]
3. Substitute [tex]\( x = 5 \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex]. We can use either [tex]\( y = 2x \)[/tex] or [tex]\( y = x + 5 \)[/tex]. Let's use [tex]\( y = 2x \)[/tex]:
[tex]\[
y = 2(5)
\][/tex]
4. Calculate [tex]\( y \)[/tex]:
[tex]\[
y = 10
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
(x, y) = (5, 10)
\][/tex]
So, the correct answer is:
A) [tex]\( (5, 10) \)[/tex]
