What is the solution to the following system of equations?x − 3y = 52x + y = 10 (5, 0) (0, 5) (7, 0) (0, 7)

1. Break Down the Problem

We need to solve the following system of equations:

1. $x - 3y = 5$
2. $2x + y = 10$

2. Relevant Concepts

To solve a system of linear equations, we can use either the substitution method, the elimination method, or graphical methods. Here, I will use the elimination method.

3. Analysis and Detail

1. Rearranging the equations:

   • From Equation 1: $x = 3y + 5$
   • Substitute $x$ from Equation 1 into Equation 2.

2. Substituting: $2(3y + 5) + y = 10$ Simplifying this: $6y + 10 + y = 10$ $7y + 10 = 10$ $7y = 10 - 10$ $7y = 0$ $y = 0$

3. Finding $x$: Substitute $y = 0$ back into Equation 1: $x - 3(0) = 5$ $x = 5$

4. Verify and Summarize

The solution to the system of equations is $(x, y) = (5, 0)$.

Final Answer

The solution to the system of equations is $(5, 0)$.