Chapter 3

Solve each system by elimination. Check your answers. $$ \left\\{\begin{aligned} x-y+z &=-1 \\ x+y+3 z &=-3 \\ 2 x-y+2 z &=0 \end{aligned}\right. $$

Find the whole number solutions of each system using tables. $$ \left\\{\begin{array}{l}{y+3 x \leq 8} \\ {y-3>2 x}\end{array}\right. $$

Describe the location of each point in coordinate space. $$ (-1,5,0) $$

Solve each system by substitution. Check your answers. \(\left\\{\begin{array}{l}{4 x+2 y=7} \\ {y=5 x}\end{array}\right.\)

Solve each system by graphing. Check your answers. $$ \left\\{\begin{array}{l}{y=x-2} \\ {y=-2 x+7}\end{array}\right. $$

Solve each system by elimination. Check your answers. $$ \left\\{\begin{aligned} x-y-2 z &=4 \\\\-x+2 y+z &=1 \\\\-x+y-3 z &=11 \end{aligned}\right. $$

Find the whole number solutions of each system using tables. $$ \left\\{\begin{array}{l}{x=y+3} \\ {x+y \leq 12}\end{array}\right. $$

Describe the location of each point in coordinate space. $$ (3,-3,4) $$

Solve each system by substitution. Check your answers. \(\left\\{\begin{array}{l}{3 c+2 d=2} \\ {d=4}\end{array}\right.\)

Solve each system by graphing. Check your answers. $$ \left\\{\begin{array}{l}{y=-x+3} \\ {y=\frac{3}{2} x-2}\end{array}\right. $$

Solve each system by elimination. Check your answers. $$ \left\\{\begin{aligned} 2 x-y+z &=-2 \\ x+3 y-z &=10 \\ x &+2 z=-8 \end{aligned}\right. $$

Find the whole number solutions of each system using tables. $$ \left\\{\begin{array}{l}{x+y<8} \\ {3 x \leq y+6}\end{array}\right. $$

Describe the location of each point in coordinate space. $$ (2,0,5) $$

Solve each system by substitution. Check your answers. \(\left\\{\begin{array}{l}{x+12 y=68} \\ {x=8 y-12}\end{array}\right.\)

Solve each system by graphing. Check your answers. $$ \left\\{\begin{aligned} 2 x+4 y &=12 \\ x+y &=2 \end{aligned}\right. $$

Solve each system by elimination. Check your answers. $$ \left\\{\begin{aligned} a+b+c &=-3 \\ 3 b-c &=4 \\ 2 a-b-2 c &=-5 \end{aligned}\right. $$

Tell whether \((-3,3)\) is a solution of each system. $$ \left\\{\begin{array}{l}{y \geq x+2} \\ {3 y<-6 x+6}\end{array}\right. $$

Describe the location of each point in coordinate space. $$ (-4,-7,-1) $$

Graph each system of constraints. Name all vertices. Then find the values of \(x\) and \(y\) that maximize or minimize the objective function. \(\left\\{\begin{array}{l}{x \leq 5} \\ {y \leq 4} \\ {x \geq 0, y \geq 0}\end{array}\right.\) Maximum for \(P=3 x+2 y\)

Solve each system by substitution. Check your answers. \(\left\\{\begin{array}{l}{4 p+2 q=8} \\ {q=2 p+1}\end{array}\right.\)

Solve each system by graphing. Check your answers. $$ \left\\{\begin{array}{l}{x=-3} \\ {y=5}\end{array}\right. $$

Solve each system by elimination. Check your answers. $$ \left\\{\begin{array}{l}{6 q-r+2 s=8} \\ {2 q+3 r-s=-9} \\ {4 q+2 r+5 s=1}\end{array}\right. $$

Tell whether \((-3,3)\) is a solution of each system. $$ \left\\{\begin{array}{l}{y-2 x \leq 1} \\ {y<-2 x-2}\end{array}\right. $$

Graph each point in coordinate space. $$ (5,0,-2) $$

Solve each system by substitution. Check your answers. \(\left\\{\begin{aligned} x+3 y &=7 \\ 2 x-4 y &=24 \end{aligned}\right.\)

Solve each system by graphing. Check your answers. $$ \left\\{\begin{array}{l}{2 x-2 y=4} \\ {y-x=6}\end{array}\right. $$

Solve each system by elimination. Check your answers. $$ \left\\{\begin{array}{l}{x-y+2 z=-7} \\ {y+z=1} \\ {x=2 y+3 z}\end{array}\right. $$

Tell whether \((-3,3)\) is a solution of each system. $$ \left\\{\begin{array}{l}{-2 y+x \leq 4} \\ {3 y<-9 x+3}\end{array}\right. $$

Graph each point in coordinate space. $$ (0,0,4) $$

Graph each system of constraints. Name all vertices. Then find the values of \(x\) and \(y\) that maximize or minimize the objective function. \(\left\\{\begin{array}{l}{x+y \leq 8} \\ {2 x+y \leq 10} \\ {x \geq 0, y \geq 0}\end{array}\right.\) Maximum for \(N=100 x+40 y\)

Solve each system by substitution. Check your answers. \(\left\\{\begin{aligned} x+6 y &=2 \\ 5 x+4 y &=36 \end{aligned}\right.\)

Solve each system by graphing. Check your answers. $$ \left\\{\begin{array}{c}{3 x+y=5} \\ {x-y=7}\end{array}\right. $$

Solve each system by elimination. Check your answers. $$ \left\\{\begin{array}{r}{x+y+2 z=3} \\ {2 x+y+3 z=7} \\ {-x-2 y+z=10}\end{array}\right. $$

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

Graph each point in coordinate space. $$ (10,-2,-5) $$

Graph each system of constraints. Name all vertices. Then find the values of \(x\) and \(y\) that maximize or minimize the objective function. \(\left\\{\begin{array}{l}{x+y \geq 6} \\ {x \leq 8} \\ {y \leq 5}\end{array}\right.\) Minimum for \(C=x+3 y\)

Solve each system by substitution. Check your answers. \(\left\\{\begin{array}{l}{3 a+b=3} \\ {2 a-5 b=-15}\end{array}\right.\)

Solve each system by graphing. Check your answers. $$ \left\\{\begin{aligned}-5 x+y &=-9 \\ x+3 y &=21 \end{aligned}\right. $$

Solve each system by elimination. Check your answers. $$ \left\\{\begin{aligned} 3 x-y+z &=3 \\ x+y+2 z &=4 \\ x+2 y+z &=4 \end{aligned}\right. $$

Graph each point in coordinate space. $$ (-1,-1,-1) $$

Solve each system by substitution. Check your answers. \(\left\\{\begin{array}{l}{t=2 r+3} \\ {5 r-4 t=6}\end{array}\right.\)

Solve each system by graphing. Check your answers. $$ \left\\{\begin{array}{l}{y=x} \\ {y-5 x=0}\end{array}\right. $$

Solve each system by elimination. Check your answers. $$ \left\\{\begin{aligned} x-2 y+3 z &=12 \\ 2 x-y-2 z &=5 \\ 2 x+2 y-z &=4 \end{aligned}\right. $$

Solve each system of inequalities by graphing. $$ \left\\{\begin{array}{l}{y \leq 3} \\ {y \leq \frac{1}{2} x+1}\end{array}\right. $$

Graph each point in coordinate space. $$ (-4,-5,3) $$

Solve each system by substitution. Check your answers. \(\left\\{\begin{array}{l}{y=2 x-1} \\ {3 x-y=-1}\end{array}\right.\)

Solve each system by graphing. Check your answers. $$ \left\\{\begin{array}{l}{x=10} \\ {x=y-10}\end{array}\right. $$

Solve each system by substitution. Check your answers. $$ \left\\{\begin{aligned} x+2 y+3 z &=6 \\ y+2 z &=0 \\ z &=2 \end{aligned}\right. $$

Solve each system of inequalities by graphing. $$ \left\\{\begin{array}{l}{y \leq 3 x+1} \\ {-6 x+2 y>5}\end{array}\right. $$

Graph each point in coordinate space. $$ (25,40,-30) $$