A System of Two Equations

Solving a system of equations in several variables is easy in Matlab. We simply make sure the variables are defined symbolically with syms and then we solve. The difference

between this and solving for one variable is that Matlab manages the result differently. For example to solve the system consisting of the two equations $2x+3y=10$ and

$5x-y=0,$ we can type:

$\%$ We syms both $x$ and $y.$ Just put a space between them!

syms $xy$

solve $(2**x+3**y==10,5**x-y==0)$

If we do this, we get something like:

ans $=$

struct with fields:

$x$: $[1x1sym]$

$y$: $[1x1sym]$

$[x,y]=$solve$(2**x+3**y==10,5**x-y==0)$

If we run this we get: Warning Note: When we do this we have actually assigned the variables $x$ and $y$ to have actual values, so really they're no longer variables. In light of this it might make more

sense to assign the result to something else, like:

$[x$ soln, ysoln$]=$ solve $(2**x+3**y==10,5**x-y==0)$

Note: The solve command returns the values in alphabetical order which is why the $x$ is returned first, and then the $y$ second.

You can also access the component variables by name. As in

ans $=$ solve $(2**x+3**y==10,5**x-y==0)$

ans. $x+$ ans. $y$

A System of Three Equations

It's probably easy to see how we would solve a system of more than two equations.

Assignment

Write a script which does all of the following in order:

Declare the variables $x$ and $y$ as symbolic.

Solve the system $5x-2y=2,7x+9y=23$ and assign the solution to a$1.$

Take the tan of the sum of the $x$ part of the solution and the $y$ part of the solution and assign the result to $z1.$

Take the logarithm base $3$ of the $y$ part of the solution and assign the result to $z2.$

Declare the variables $s,t,$ and $u$ as symbolic.

Solve the system $2s+t+u=10,4s-t+7u=4,s-u=1$ and assign the solution to the variables ssoln, tsoln, and usoln.

Calculate $e^{s-t+u}$ using the ssoln, tsoln, and usoln parts of the solution and assign the result to $z3.$

Calculate $tan(s+2u)$ using the ssoln and usoln parts of the solution and assign the result to $z4.$Write a script which does all of the following in order:

Declare the variables $x$ and $y$ as symbolic.

Solve the system $5x-2y=2,7x+9y=23$ and assign the solution to a$1.$

Take the tan of the sum of the $x$ part of the solution and the $y$ part of the solution and assign the result to $z1.$

Take the logarithm base $3$ of the $y$ part of the solution and assign the result to $z2.$

Declare the variables $s,t,$ and $u$ as symbolic.

Solve the system $2s+t+u=10,4s-t+7u=4,s-u=1$ and assign the solution to the variables ssoln, tsoln, and usoln.

Calculate $e^{s-t+u}$ using the ssoln, tsoln, and usoln parts of the solution and assign the result to $z3.$

Calculate $tan(s+2u)$ using the ssoln and usoln parts of the solution and assign the result to $z4.$

syms $x$ y

a$1=$ solve $(5**x-2**y==2,7**x+9**y==23)$

$z1=tan(a1.x+a1.y)$

please help with the rest