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Substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer's rule. Use each method at least once when solving the systems below. include solutions with nonreal complex number components. For systems with infinitely many solutions, write the solution set using an arbitrary variable.
$2x+3y+4z=3$
$-4x+2y-6z=2$
$4x+3z=0$

Transform the given differential equation or system into an equivalent system of first-order differential equations.

One cake recipe calls for ${\displaystyle \frac{2}{3}}$ cup of sugar. Another recipe calls for ${\displaystyle 1\frac{1}{4}}$ cups of sugar. How many cups of sugar are needed to make both cakes?

Starting with the geometric series $\sum _{n=0}^{\mathrm{\infty }}{x}^n$, find the sum of the series
$\sum _{n=1}^{\mathrm{\infty }}n{x}^{n-1},|x|<1$

Discuss the continuity of the function and evaluate the limit of f(x, y) (if it exists) as ${\displaystyle (x,y)\to (0,0).f(x,y)=1-\frac{\cos (x^2+y^2)}{x^2+y^2}}$

Determine if a geometric series converges or diverges
$10-4+1.6-0.64+...$ 
If it convergent, find the sum.

h is related to one of the parent functions described in this chapter. Describe the sequence of transformations from f to h. $h(x)=(x-2{)}^3+2$

Suppose that f is an exponential function with percentage growth rate of 5% and that $f(0)=4$. Find a formula for f(x).