Write a MATLAB script that will accomplish the tasks listed below.

Use clc to clear the command window, clear to clear the workspace, and close all to close any

open figures at the beginning of your script.

Separate code for each task by sections and label the sections.

Comment your work.

Name the m $-$file LastName$\_$Lab$4.$m where LastName is your last name.

Submit your lab m$-$file using Canvas.

Feel free to discuss the lab assignment, but you must do your own work.

Project Code $-$ Linear Systems of Equations Part $1$

This code will evolve over several labs and allow for you to build your code and enhance it over time. This

week we will begin by building an understanding of:

What a system of equations is

What possible solutions exist for a system of equations

How to solve $22$ systems, a system of two equations with two unknowns, with:

a$.$ Graphical Methods

b$.$ Gauss Elimination

System $1$

System $2$

System $3$

$3x+2y=18$

$-x+2y=2$

$-\frac{1}{2}x+2y=2$

$-\frac{1}{2}x+y=1$

$-\frac{1}{2}x+2y=2$

$-x+2y=1$

Graphical Interpretation

Each of the above systems provide a relationship between two parameters, $x$ and $y,$ the values of which are

not known but for which two equations relate the parameters. Given only one of these equations, there would

be infinite pairs of $x$ and $y$ values which would satisfy the equation. How many solutions are possible with two

equations? To begin to understand this, create separate plots for each system where each equation can be

viewed as a line. Label the plots adding titles and axis labels. Are there values for x and y which exist that

are solutions to each system?

Explicit Solution

Given a general set of equations below, solve for the x value for which y values are equal.

$a_{11}x+a_{12}y=c_1,$ Eqn.$(1)$

$a_{21}x+a_{22}y=c_2,$ Eqn.$(2)$