91Ó°ÊÓ

a. Graph the equations in the system. b. Solve the system by using the substitution method. (See Examples \(1-2\) ) $$ \begin{array}{l} y=\sqrt{x} \\ x^{2}+y^{2}=20 \end{array} $$

An athlete burns 10 calories per minute running and 8 calories per minute lifting weights. Write an objective function \(z=f(x, y)\) that represents the total number of calories burned by running for \(x\) minutes and lifting weights for \(y\) minutes.

Determine whether the ordered pair is a solution to the inequality. \(2 x+3 y>6\) a. (-3,3) b. (5,-1) c. (0,2)

Determine if the ordered triple is a solution to the system of equations. \(-x-y+z=3\) \(3 x+4 y-z=1\) \(5 x+7 y-z=-1\) a. (1,2,6) b. (3,-1,5)

A system of equations is given in which each equation is written in slope- intercept form. Determine the number of solutions. If the system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. $$ \begin{array}{l} y=\frac{1}{2} x+3 \\ y=2 x+\frac{1}{3} \end{array} $$

Solve the system of equations by using the substitution method. (See Example 2\()\) $$ \begin{array}{rr} x+3 y= & 5 \\ 3 x-2 y= & -18 \end{array} $$

A courier company makes deliveries with two different trucks. Truck A costs \(\$ 0.62 / \mathrm{mi}\) to operate and truck \(\mathrm{B}\) costs \(\$ 0.50 / \mathrm{mi}\) to operate. Write an objective function \(z=f(x, y)\) that represents the total cost for driving truck A for \(x\) miles and driving truck \(\mathrm{B}\) for \(y\) miles.

Solve the system of equations. If a system does not have one unique solution, determine the number of solutions to the system. $$ \begin{aligned} x-2 y+z &=-9 \\ 3 x+4 y+5 z &=9 \\ -2 x+3 y-z &=12 \end{aligned} $$

Determine whether the ordered pair is a solution to the inequality. \(y \geq(x-3)^{2}\) a. (-3,30) b. (1,4) c. (5,5)

Determine whether the ordered pair is a solution to the inequality. \(y \geq(x-3)^{2}\) a. (-3,30) b. (1,4) c. (5,5)