Solve Simultaneous Equations: 2x + y = 9 and x = 5

Solve the following equations:

$\begin{cases} 2x+y=9 \\ x=5 \end{cases}$

To solve this system of equations, we'll use the substitution method as follows:

• Step 1: Identify the given information.
  We have two equations: $\begin{cases} 2x + y = 9 \\ x = 5 \end{cases}$
• Step 2: Substitute $x = 5$ into the first equation.
  The equation becomes: $2(5) + y = 9$ which simplifies to: $10 + y = 9$
• Step 3: Solve for $y$.
  Subtract 10 from both sides: $y = 9 - 10$ $y = -1$
• Step 4: Verify the solution.
  Substituting $x = 5$ and $y = -1$ back into the first equation confirms the solution:
  $2(5) + (-1) = 10 - 1 = 9$

Both equations are satisfied with $x = 5$ and $y = -1$.

Therefore, the solution to the system of equations is $x = 5, y = -1$.