The image you've provided contains a system of equations that we need to solve:

1. $2x - 6y = -16$
2. $x + 3y = 16$

Step 1: Solve the second equation for $x$

From the second equation $x + 3y = 16$, we can solve for $x$:

$x = 16 - 3y$

Step 2: Substitute into the first equation

Now substitute $x = 16 - 3y$ into the first equation $2x - 6y = -16$:

$2(16 - 3y) - 6y = -16$

Step 3: Simplify and solve for $y$

Now expand and simplify the equation:

$32 - 6y - 6y = -16$

$32 - 12y = -16$

Subtract 32 from both sides:

$-12y = -48$

Now divide both sides by -12:

$y = 4$

Step 4: Substitute $y = 4$ into the second equation to solve for $x$

Substitute $y = 4$ back into $x + 3y = 16$:

$x + 3(4) = 16$

$x + 12 = 16$

Subtract 12 from both sides:

$x = 4$

Final Answer:

The solution is $x = 4$ and $y = 4$.

Thus, the solution in ordered pair form is $(4, 4)$.

Would you like further clarification or details on any of the steps?

Related Questions:

1. How would you solve a system of equations using the substitution method?
2. What is the elimination method for solving systems of equations?
3. How can you graph a system of linear equations to find the solution visually?
4. How would the solution change if one of the equations was nonlinear?
5. How can you check your solution to a system of equations?

Tip:

When solving systems of equations, be careful with signs and coefficients. It's easy to make small mistakes, so double-check your calculations!