Chapter 3

Solve each system. \(\left\\{\begin{array}{l}{\frac{x}{3}+\frac{4 y}{3}=300} \\ {3 x-4 y=300}\end{array}\right.\)

Graph each equation. $$ 2 x+3 y-z=12 $$

Solve each system. \(\left\\{\begin{array}{l}{0.02 a-1.5 b=4} \\ {0.5 b-0.02 a=1.8}\end{array}\right.\)

Graph each equation in three-dimensional coordinate space. $$ y=0 $$

Solve each system. \(\left\\{\begin{array}{l}{4 y=2 x} \\ {2 x+y=\frac{x}{2}+1}\end{array}\right.\)

Which point is NOT on the graph of \(2 x+3 y-z-12=0 ?\) $$ \begin{array}{llll}{\text { A. }(6,0,0)} & {\text { B. }(3,3,3)} & {\text { C. }(0,4,0)} & {\text { D. }(1,1,7)}\end{array} $$

The equation \(3 x-4 y=2\) and which equation below form a system with no solutions? A. \(2 y=1.5 x-2\) B. \(2 y=1.5 x-1\) C. \(3 x+4 y=2\) D. \(4 y-3 x=-2\)

Write a system of linear equations with the solution set \(\\{(x, y) | y=5 x+2\\}\)

Which point is NOT on the plane with equation \(-2 x-3 y+5 z=7 ?\) \(F_{ .}(1,2,3)\) G. \((-2,-3,5)\) \(H \cdot(-2,4,3)\) \ \((-4,2,1)\)

For each system, choose the method of solving that seems easier to use. Explain why you made each choice. \(\left\\{\begin{aligned} 3 x-5 y &=26 \\\\-2 x-3 y &=-11 \end{aligned}\right.\)

What are the intercepts of \(-3 x+5 y-2 z=60 ?\) $$ \begin{array}{ll}{\text { A. } x=-180, y=300, z=-120} & {\text { B. } x=-20, y=12, z=-30} \\ {\text { C. } x=-3, y=5, z=-2} & {\text { D. } x=-60, y=60, z=-60}\end{array} $$

For each system, choose the method of solving that seems easier to use. Explain why you made each choice. \(\left\\{\begin{array}{l}{y=\frac{2}{3} x-3} \\ {-x+3 y=18}\end{array}\right.\)

Economics Resarch shows that in a certain market only 2000 widgets can be sold at \(\$ 8\) each, but if the price is reduced to \(\$ 3,\) then \(10,000\) can be sold. a. Let \(p\) represent price and \(n\) represent the number of widgets. Identify the independent variable and the dependent variable. b. Use the information above to write a linear demand equation. c. A shop can make 2000 widgets for \(\$ 5\) each and \(20,000\) widgets for \(\$ 2\) each. Use this information to write a linear supply equation. d. Find the equilibrium point where supply is equal to demand and profit is a maximum. Explain the meaning of the coordinates of this point within the context of the exercise.

Graph each equation. $$ y=|x+4| $$

How would you test whether \((2,-2)\) is a solution of the system?

What is the \(x y\) -trace of \(2 x-4 y+z=8 ?\) \ \(F .-4 y+z=8\) G. \(x-2 y=4\) H. \(2 x+z=8\) J. \(z=8\)

For each system, choose the method of solving that seems easier to use. Explain why you made each choice. \(\left\\{\begin{aligned} 2 m+3 n &=12 \\\\-5 m+n &=-13 \end{aligned}\right.\)

Graph each equation. $$ y=|3 x-2| $$

Solve each system by elimination or substitution. $$ \left\\{\begin{array}{l}{y=3 x+1} \\ {2 x-y=8}\end{array}\right. $$

For each system, choose the method of solving that seems easier to use. Explain why you made each choice. \(\left\\{\begin{array}{l}{3 x-y=5} \\ {y=4 x+2}\end{array}\right.\)

Graph each equation. $$ y=\left|\frac{1}{2} x+3\right|-2 $$

Solve each system by elimination or substitution. $$ \left\\{\begin{array}{r}{3 x+y=4} \\ {2 x-4 y=7}\end{array}\right. $$

For each system, choose the method of solving that seems easier to use. Explain why you made each choice. \(\left\\{\begin{array}{l}{2 x-3 y=4} \\ {2 x-5 y=-6}\end{array}\right.\)

Graph each equation. $$ y=|x-2|+1 $$

Solve each system by elimination or substitution. $$ \left\\{\begin{array}{l}{-x+5 y=3} \\ {2 x-10 y=4}\end{array}\right. $$

Graph each inequality. $$ y \leq x-3 $$

For each system, choose the method of solving that seems easier to use. Explain why you made each choice. \(\left\\{\begin{array}{l}{6 x-3 y=3} \\ {5 x-5 y=10}\end{array}\right.\)

What is the solution of the system? \(\left\\{\begin{array}{c}{5 x+6 y=-24} \\\ {-2 x+3 y=15} \\ {\text { H. }(-6,1)}\end{array}\right.\) $$ \begin{array}{llll}{\text { F. }(6,-1)} & {\text { G. }(6,1)} & {\text { H. }(-6,1)} & {\text { J. }(-6,-1)}\end{array} $$

Graph each equation. $$ y=|2 x+1| $$

Solve each system by elimination or substitution. $$ \left\\{\begin{aligned} 2 x+4 y &=-8 \\\\-5 x+4 y &=6 \end{aligned}\right. $$

Graph each inequality. $$ 3 y-x>-4 $$

Graph each equation. $$ y=|x+3|-2 $$

Solve each system by elimination or substitution. $$ \left\\{\begin{array}{l}{y-3=x} \\ {4 x+y=-2}\end{array}\right. $$

Graph each inequality. $$ 2 x-y \geq 0 $$

Solve each inequality. Graph the solution on a number line. $$ -4 x+3 \leq 9 $$

Solve each system by elimination or substitution. $$ \left\\{\begin{array}{l}{2=4 y-3 x} \\ {5 x=2 y-3}\end{array}\right. $$

Probability Your town has a drawing for 50 summer jobs. Including you, 150 students apply. a. What is the probability that you will get one of the jobs? b. You and a friend apply. What is the probability that you both get jobs?

A theater production costs \(\$ 40,000\) plus \(\$ 2800\) per performance. A sold- out performance brings in \(\$ 3675 .\) How many sold-out performances will the production need to break even?

Graph each inequality on a coordinate plane. $$ 3 x-4 y \geq 16 $$

Solve each inequality. Graph the solution on a number line. $$ -(x+4)-3 \geq 11 $$

For each function, \(y\) varies directly as \(x\) If \(y=-6\) when \(x=-2,\) find \(y\) when \(x=3\)

The equation \(F=\frac{9}{5} C+32\) relates temperatures on the Celsius and Fahrenheit scales. Does any temperature have the same number reading on both scales? If so, what is the number?

Graph each inequality on a coordinate plane. $$ -5 x>8 y+4 $$

Solve each inequality. Graph the solution on a number line. $$ 2(3 x-1)

For each function, \(y\) varies directly as \(x\) If \(y=-8\) when \(x=2,\) find \(x\) when \(y=2\)

Find the value of \(a\) that makes each system a dependent system. \(\left\\{\begin{array}{l}{y=3 x+a} \\ {3 x-y=2}\end{array}\right.\)

Graph each inequality on a coordinate plane. $$ x<-4 $$

Solve each inequality. Graph the solution on a number line. $$ 6-2 x>2 $$

For each function, \(y\) varies directly as \(x\) If \(y=4\) when \(x=7,\) find \(y\) when \(x=-14\)

Find the value of \(a\) that makes each system a dependent system. \(\left\\{\begin{array}{l}{3 y=2 x} \\ {6 y-a-4 x=0}\end{array}\right.\)