Verify if (2, 8) is a Solution to the Linear System $\begin{cases} x + y = 10 \\ 2x + 3y = 28 \end{cases}$

Question

Test the given solution (2, 8) to confirm it works for the system: $\begin{cases} x + y = 10 \ 2x + 3y = 28 \end{cases}$

Accepted Answer

The solution (2, 8) is valid for the system of equations.

Answer

Step 1: Identify the values from the solution: $x = 2$, $y = 8$. Step 2: Substitute into the first equation $x + y = 10$: $2 + 8 = 10$, which simplifies to $10 = 10$. This is a true statement, so the solution satisfies the first equation. Step 3: Substitute into the second equation $2x + 3y = 28$: $2(2) + 3(8) = 4 + 24 = 28$, which simplifies to $28 = 28$. This is a true statement, so the solution satisfies the second equation. Step 4: Since the solution satisfies both equations in the system, it is a valid solution.