The images you uploaded contain mathematical problems. I'll extract the details from each image and provide solutions.

First Image:

1. Equation: $x^2 = 4$
2. Expressions: $y = \frac{x}{4} + 1$ $\frac{y}{2} = 16 - 2x$
3. Task: The question asks to find the solution to the given system of equations, $\left( x, y \right)$.

Second Image:

1. Equation: $x^2 = 9$
2. Expressions: $y = \frac{x}{3} + 1$ $\frac{y}{2} = 16 - 3x$
3. Task: The question also asks to find the solution to the given system of equations, $\left( x, y \right)$.

Let's solve both systems of equations:

First System:

1. Solve for $x$: $x^2 = 4 \implies x = \pm 2$
2. Substitute $x = 2$ into the first equation for $y$: $y = \frac{2}{4} + 1 = 0.5 + 1 = 1.5$
3. Substitute $x = 2$ into the second equation for $y$: $\frac{y}{2} = 16 - 4 \implies \frac{y}{2} = 12 \implies y = 24$ So, the equations are inconsistent, as the solutions for $y$ do not match.

Second System:

1. Solve for $x$: $x^2 = 9 \implies x = \pm 3$
2. Substitute $x = 3$ into the first equation for $y$: $y = \frac{3}{3} + 1 = 1 + 1 = 2$
3. Substitute $x = 3$ into the second equation for $y$: $\frac{y}{2} = 16 - 9 \implies \frac{y}{2} = 7 \implies y = 14$ Again, the solutions are inconsistent, as the solutions for $y$ do not match.

Conclusion:

Both systems of equations are inconsistent, meaning there are no solutions where the given conditions hold simultaneously.

Would you like more details or have any questions? Here are some additional related questions:

1. How can you determine if a system of equations is consistent?
2. What are the different types of solutions possible in a system of linear equations?
3. How does the substitution method work for solving systems of equations?
4. What is the significance of finding no solutions in a system of equations?
5. How do you graphically represent a system of equations?
6. What does it mean if two equations are parallel in a system of equations?
7. How can you check your solutions when solving a system of equations?
8. What are the implications of using different methods (substitution, elimination) on solving systems of equations?

Tip: When solving a system of equations, ensure that the solution satisfies all original equations to confirm consistency.