91Ó°ÊÓ

Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in the ordered-pair form given in Example 3. $$\left\\{\begin{array}{l} 2 x-3 y=9 \\ 4 x+3 y=9 \end{array}\right.$$

Perform the matrix operation, or if it is impossible, explain why. $$\left[\begin{array}{rr} 1 & 2 \\ -1 & 4 \end{array}\right]\left[\begin{array}{rrr} 1 & -2 & 3 \\ 2 & 2 & -1 \end{array}\right]$$

Graph the inequality. $$4 x+5 y<20$$

Use back-substitution to solve the triangular system. $$\left\\{\begin{array}{r} 2 x-y+6 z=5 \\ y+4 z=0 \\ -2 z=1 \end{array}\right.$$

Use the elimination method to find all solutions of the system of equations. $$\left\\{\begin{array}{r}x+2 y=5 \\\2 x+3 y=8\end{array}\right.$$

A matrix is given. (a) Determine whether the matrix is in row-echelon form. (b) Determine whether the matrix is in reduced row-echelon form. (c) Write the system of equations for which the given matrix is the augmented matrix. $$\left[\begin{array}{llll} 1 & 2 & 8 & 0 \\ 0 & 1 & 3 & 2 \\ 0 & 0 & 0 & 0 \end{array}\right]$$

Use back-substitution to solve the triangular system. $$\left\\{\begin{aligned} 4 x\quad\quad+3 z &=10 \\ 2 y-\quad z &=-6 \\ \frac{1}{2} z &=4 \end{aligned}\right.$$

Express the function (or rule) in words. $$k(x)=\sqrt{x+2}$$

Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in the ordered-pair form given in Example 3. $$\left\\{\begin{array}{c} 3 x+2 y=0 \\ -x-2 y=8 \end{array}\right.$$

Graph the inequality. $$-x^{2}+y \geq 10$$