https://r2.erweima.ai/mathbot/image/1718349016990zqoti5hm.png

To solve the system of equations given in the image:

\[
\begin{cases}
2x + y = 5 \\
x + 3y = 5
\end{cases}
\]

we need to find the values of \(x\) and \(y\), and then compute \(x + y\).

First, let's multiply the second equation by 2 to align the coefficients of \(x\):

\[
2(x + 3y) = 2 \cdot 5 \\
2x + 6y = 10
\]

Now we have the system:

\[
\begin{cases}
2x + y = 5 \\
2x + 6y = 10
\end{cases}
\]

Subtract the first equation from the second:

\[
(2x + 6y) - (2x + y) = 10 - 5 \\
5y = 5 \\
y = 1
\]

Substitute \(y = 1\) back into the first equation to find \(x\):

\[
2x + 1 = 5 \\
2x = 4 \\
x = 2
\]

Now we find \(x + y\):

\[
x + y = 2 + 1 = 3
\]

Therefore, the value of \(x + y\) is \(3\).

Would you like more details or have any questions? Here are some more questions you might find interesting:

1. How to solve a system of linear equations using substitution?
2. How to solve a system of linear equations using elimination?
3. What are the methods to solve a system of equations graphically?
4. How to determine if a system of equations has no solution, one solution, or infinitely many solutions?
5. How to solve systems of equations using matrices?

**Tip:** When solving systems of equations, always check your solution by substituting the values back into the original equations to ensure they satisfy both equations.

Learn how to solve the system of linear equations 2x + y = 5 and x + 3y = 5 with a step-by-step solution. This problem covers key concepts in systems of linear equations, including the substitution and elimination methods. Suitable for high school students.

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