https://file.aiquickdraw.com/mathbot/file/17285129317165lcebwbd.jpg

The system of equations shown in the image is:

\[
\begin{aligned}
1) & \quad x + 4y = 14 \\
2) & \quad 16y = -56 + 4x
\end{aligned}
\]

We are asked to solve this system using substitution. Let's go step by step.

### Step 1: Solve one equation for one variable
We can easily solve the first equation for \(x\):
\[
x = 14 - 4y
\]

### Step 2: Substitute the expression for \(x\) into the second equation
Substitute \(x = 14 - 4y\) into the second equation:
\[
16y = -56 + 4(14 - 4y)
\]

Now expand and simplify:
\[
16y = -56 + 56 - 16y
\]
\[
16y = -16y
\]

### Step 3: Solve the simplified equation
Add \(16y\) to both sides:
\[
32y = 0
\]

Divide both sides by 32:
\[
y = 0
\]

### Step 4: Substitute \(y = 0\) into the first equation
Substitute \(y = 0\) into the first equation \(x + 4y = 14\):
\[
x + 4(0) = 14
\]
\[
x = 14
\]

### Final Answer:
The solution is:
\[
x = 14, \quad y = 0
\]

There is **one solution**, which is \((14, 0)\).

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How can you verify if the solution to a system of equations is correct?
2. What happens when a system has no solution? How can you identify this?
3. How do you solve a system of equations using the elimination method?
4. What are some real-life applications of solving systems of equations?
5. Can you explain the differences between dependent, independent, and inconsistent systems?

**Tip:** When solving systems of equations, substitution works best if one of the equations is already solved for a variable, or can easily be solved for one!

Solve the system of equations using substitution:
1) x + 4y = 14
2) 16y = -56 + 4x

This page provides a step-by-step solution to solving the system of equations x + 4y = 14 and 16y = -56 + 4x using the substitution method. Key algebraic concepts such as substitution, solving for one variable, and simplifying equations are covered. Suitable for Grades 8-10.

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