Chapter 3

Without graphing, classify each system as independent, dependent, or inconsistent. $$ \left\\{\begin{array}{l}{2 y-x=4} \\ {\frac{1}{2} x-y=2}\end{array}\right. $$

Solve each system. $$ \left\\{\begin{aligned} x-3 y+2 z &=11 \\\\-x+4 y+3 z &=5 \\ 2 x-2 y-4 z &=2 \end{aligned}\right. $$

Solve each system of inequalities by graphing. $$ \left\\{\begin{array}{l}{5 y \geq 2 x-5} \\ {y<|x+3|}\end{array}\right. $$

Solve each system by elimination. \(\left\\{\begin{array}{l}{5 x+3 y=30} \\ {3 x+3 y=18}\end{array}\right.\)

Graph and solve each system. Where necessary, estimate the solution. $$ \left\\{\begin{array}{l}{3=4 y+x} \\ {4 y=-x+3}\end{array}\right. $$

Solve each system. $$ \left\\{\begin{aligned} x+2 y+z &=4 \\ 2 x-y+4 z &=-8 \\\\-3 x+y-2 z &=-1 \end{aligned}\right. $$

Solve each system of inequalities by graphing. $$ \left\\{\begin{array}{l}{y \geq-3 x+3} \\ {y>|x+2|}\end{array}\right. $$

Multiple Choice Suppose you have \(\$ 20\) to spend on party decorations. Balloons are \(\$ .05\) each, streamers are \(\$ .25\) each, and noisemakers are \(\$ .4\) , streach. Which equation best models this situation? $$ \begin{array}{l}{\text { A) } 5 b+25 s+40 n=20} \\ {\text { (B) } 20(b+s+n)=0.05+0.25+0.4} \\ {\text { C } 0.05 b+0.25 s+0.4 n=20} \\ {\text { D) } 0.05 b+0.25 s+0.4 n+20=0}\end{array} $$

Solve each system by elimination. \(\left\\{\begin{array}{l}{x-14=-y} \\ {x-y=2}\end{array}\right.\)

Graph and solve each system. Where necessary, estimate the solution. $$ \left\\{\begin{array}{l}{x-2 y+1=0} \\ {x+4 y-6=0}\end{array}\right. $$

Solve each system of inequalities by graphing. $$ \left\\{\begin{array}{l}{-2 y<4 x+2} \\ {y>|2 x+1|}\end{array}\right. $$

What are the vertices of the feasible region bounded by the constraints at the right? \(\left\\{\begin{array}{l}{x+y \leq 3} \\ {2 x+y \leq 4} \\ {x \geq 0, y \geq 0}\end{array}\right.\)

Solve each system by elimination. \(\left\\{\begin{array}{l}{3 x+2 y=6} \\ {3 x+3=y}\end{array}\right.\)

Graph and solve each system. Where necessary, estimate the solution. $$ \left\\{\begin{array}{l}{3 x+6 y-12=0} \\ {x+2 y=8}\end{array}\right. $$

Solve each system. $$ \left\\{\begin{aligned} 4 A+2 U+I &=2 \\ 5 A-3 U+2 I &=17 \\ A-5 U &=3 \end{aligned}\right. $$

Solve each system of inequalities by graphing. \(\left\\{\begin{array}{l}{y<-2 x+8} \\ {3 y \geq 4 x-6}\end{array}\right.\)

Solve each system by elimination. \(\left\\{\begin{array}{l}{5 x-y=4} \\ {2 x-y=1}\end{array}\right.\)

Graph and solve each system. Where necessary, estimate the solution. $$ \left\\{\begin{aligned}-x+3 y &=6 \\ 2 x-y &=8 \end{aligned}\right. $$

Solve each system. $$ \left\\{\begin{aligned} 4 x-2 y+5 z &=6 \\ 3 x+3 y+8 z &=4 \\ x-5 y-3 z &=5 \end{aligned}\right. $$

Solve each system of inequalities by graphing. \(\left\\{\begin{array}{c}{x-2 y \geq 11} \\ {5 x+4 y<27}\end{array}\right.\)

Sketch the graph of each equation. $$ 32 x+16 y-8 z=32 $$

Solve each system by elimination. \(\left\\{\begin{array}{l}{2 r+s=3} \\ {4 r-s=9}\end{array}\right.\)

Graph and solve each system. Where necessary, estimate the solution. $$ \left\\{\begin{array}{l}{3 x+y=3} \\ {2 x-y=7}\end{array}\right. $$

Solve each system. $$ \left\\{\begin{array}{l}{2 \ell+2 w+h=72} \\ {\ell=3 w} \\ {h=2 w}\end{array}\right. $$

In Exercises \(30-39\) , identify the inequalities \(\mathbf{A}, \mathbf{B},\) and \(\mathbf{C}\) for which the given ordered pair is a solution. A. \(x+y \leq 2\) (GRAPH NOT COPY) B. \(y \leq \frac{3}{2} x-1\) (GRAPH NOT COPY) C. \(y>-\frac{1}{3} x-2\) (GRAPH NOT COPY) $$ (0,0) $$

Solve each system of inequalities by graphing. \(\left\\{\begin{array}{l}{2 x+6 y>12} \\ {3 x+9 y \leq 27}\end{array}\right.\)

Solve each system by elimination. \(\left\\{\begin{aligned} 4 x-6 y &=-26 \\\\-2 x+3 y &=13 \end{aligned}\right.\)

Graph and solve each system. Where necessary, estimate the solution. $$ \left\\{\begin{array}{l}{2 x+3 y=6} \\ {4 x=6 y+3}\end{array}\right. $$

Solve each system. $$ \left\\{\begin{aligned} 3 x+2 y-z &=17.8 \\ x-3 y+2 z &=7.9 \\ 2 x+y-3 z &=3.9 \end{aligned}\right. $$

Solve each system of inequalities by graphing. \(\left\\{\begin{array}{c}{2 y+x<4} \\ {y-2 x \geq 4}\end{array}\right.\)

Solve each system by elimination. \(\left\\{\begin{aligned} 9 a-3 d &=3 \\\\-3 a+d &=-1 \end{aligned}\right.\)

Graph and solve each system. Where necessary, estimate the solution. $$ \left\\{\begin{array}{l}{10-3 x=-3 y} \\ {2=2 x+y}\end{array}\right. $$

Solve each system. $$ \left\\{\begin{aligned} x+2 y &=2 \\ 2 x+3 y-z &=-9 \\ 4 x+2 y+5 z &=1 \end{aligned}\right. $$

Solve each system of inequalities by graphing. \(\left\\{\begin{array}{l}{y+5 \geq-2 x} \\ {y-x \geq-2}\end{array}\right.\)

Solve each system by elimination. \(\left\\{\begin{array}{l}{2 a+3 b=12} \\ {5 a-b=13}\end{array}\right.\)

Graph and solve each system. Where necessary, estimate the solution. $$ \left\\{\begin{array}{l}{3 x=-5 y+4} \\ {250+150 x=300}\end{array}\right. $$

Solve each system. $$ \left\\{\begin{aligned} 3 x+2 y+2 z &=-2 \\ 2 x+y-z &=-2 \\ x-3 y+z &=0 \end{aligned}\right. $$

Solve each system of inequalities by graphing. \(\left\\{\begin{array}{l}{2 y-4 x<6} \\ {6 x<3 y+12}\end{array}\right.\)

Sketch the graph of each equation and find the equation of each trace. $$ 6 x+6 y-12 z=36 $$

Graph and solve each system. Where necessary, estimate the solution. $$ \left\\{\begin{aligned} x+3 y &=6 \\ 6 y+2 x &=12 \end{aligned}\right. $$

Solve each system. $$ \left\\{\begin{aligned} 6 x+y-4 z &=-8 \\ \frac{y}{4}-\frac{z}{6} &=0 \\ 2 x &-z=-2 \end{aligned}\right. $$

Solve each system by elimination. \(\left\\{\begin{array}{l}{20 x+5 y=120} \\ {10 x+7.5 y=80}\end{array}\right.\)

Graph and solve each system. Where necessary, estimate the solution. $$ \left\\{\begin{array}{l}{2 y+x=8} \\ {y-2 x=-6}\end{array}\right. $$

Solve each system. $$ \left\\{\begin{array}{l}{4 y+2 x=6-3 z} \\ {x+z-2 y=-5} \\ {x-2 z=3 y-7}\end{array}\right. $$

Evaluate each expression for \(a=3\) and \(b=-5\) \(2 a+b\)

Solve each system by elimination. \(\left\\{\begin{aligned} 6 x-2 y &=11 \\\\-9 x+3 y &=16 \end{aligned}\right.\)

Graph and solve each system. Where necessary, estimate the solution. $$ \left\\{\begin{array}{l}{y=-2 x+6} \\ {x-3 y=-6}\end{array}\right. $$

Solve each system. $$ \left\\{\begin{array}{l}{5 z+4 y=4} \\ {3 x-2 y=0} \\ {x+3 z=-8}\end{array}\right. $$

Evaluate each expression for \(a=3\) and \(b=-5\). \(a-b\)

Sketch the graph of each equation and find the equation of each trace. $$ 25 x+125 y-25 z=125 $$