Chapter 5

Solve the system by the method of substitution. $$\left\\{\begin{aligned} x+2 y &=1 \\ 5 x-4 y &=-23 \end{aligned}\right.$$

Sketch the graph of the inequality. $$x^{2}+y^{2} \leq 4$$

Solve the system of equations. $$\left\\{\begin{aligned} x+2 y-7 z &=-4 \\ 2 x+y+z &=13 \\ 3 x+9 y-36 z &=-33 \end{aligned}\right.$$

Solve the system by elimination Then state whether the system is consistent inconsistent. $$\left\\{\begin{array}{r}2 u+v=120 \\ u+2 v=120\end{array}\right.$$

Solve the system by the method of substitution. $$\left\\{\begin{array}{l}2 x-y+2=0 \\ 4 x+y-5=0\end{array}\right.$$

Sketch the graph of the inequality. $$x^{2}+y^{2}>4$$

Solve the system of equations. $$\left\\{\begin{aligned} 2 x+y-3 z &=4 \\ 4 x &+2 z=10 \\\\-2 x+3 y-13 z &=-8 \end{aligned}\right.$$

Solve the system by elimination Then state whether the system is consistent inconsistent. $$\left\\{\begin{array}{l}5 u+6 v=24 \\ 3 u+5 v=18\end{array}\right.$$

Solve the system by the method of substitution. $$\left\\{\begin{aligned} 6 x-3 y-4 &=0 \\ x+2 y-4 &=0 \end{aligned}\right.$$

Maximize the objective function subject to the constraints \(3 x+y \leq 15,4 x+3 y \leq 30\) \(x \geq 0\), and \(y \geq 0\) $$z=2 x+y$$

Sketch the graph of the inequality. $$x^{2}+(y-2)^{2}<16$$

Solve the system of equations. $$\left\\{\begin{array}{rr}x+4 z & =13 \\ 4 x-2 y+z= & 7 \\ 2 x-2 y-7 z & =-19\end{array}\right.$$

Solve the system by elimination Then state whether the system is consistent inconsistent. $$\left\\{\begin{array}{l}4 b+3 m=3 \\ 3 b+11 m=13\end{array}\right.$$

Solve the system by the method of substitution. $$\left\\{\begin{aligned} x-y &=7 \\ 2 x+y &=23 \end{aligned}\right.$$

Maximize the objective function subject to the constraints \(3 x+y \leq 15,4 x+3 y \leq 30\) \(x \geq 0\), and \(y \geq 0\) $$z=5 x+y$$

Sketch the graph of the inequality. $$y-(x-3)^{3} \geq 0$$

Solve the system of equations. $$\left\\{\begin{aligned} 4 x-y+5 z &=11 \\ x+2 y-z &=5 \\ 5 x-8 y+13 z &=7 \end{aligned}\right.$$

Solve the system by elimination Then state whether the system is consistent inconsistent. $$\left\\{\begin{array}{l}3 b+3 m=7 \\ 3 b+5 m=3\end{array}\right.$$

Solve the system by the method of substitution. $$\left\\{\begin{aligned} x-2 y &=-2 \\ 3 x-y &=6 \end{aligned}\right.$$

Maximize the objective function subject to the constraints \(3 x+y \leq 15,4 x+3 y \leq 30\) \(x \geq 0\), and \(y \geq 0\) $$z=4 x+3 y$$

Graph the solution set of the system of inequalities. $$\left\\{\begin{aligned} x+y & \leq 2 \\\\-x+y & \leq 2 \\ y & \geq 0 \end{aligned}\right.$$

Solve the system of equations. $$\left\\{\begin{aligned} x+4 z &=1 \\ x+y+10 z &=10 \\ 2 x-y+2 z &=-5 \end{aligned}\right.$$

Solve the system by elimination Then state whether the system is consistent inconsistent. $$\left\\{\begin{aligned} 6 r-5 s &=3 \\\\-1.2 r+s &=0.5 \end{aligned}\right.$$

Solve the system by the method of substitution. $$\left\\{\begin{array}{l}0.3 x-0.4 y-0.33=0 \\ 0.1 x+0.2 y-0.21=0\end{array}\right.$$

Maximize the objective function subject to the constraints \(3 x+y \leq 15,4 x+3 y \leq 30\) \(x \geq 0\), and \(y \geq 0\) $$z=3 x+y$$

Graph the solution set of the system of inequalities. $$\left\\{\begin{aligned} 3 x+2 y &<6 \\ x &>1 \\ y &>0 \end{aligned}\right.$$

Solve the system of equations. $$\left\\{\begin{aligned} 3 x-2 y-6 z &=4 \\\\-3 x+2 y+6 z &=1 \\ x-y-5 z &=3 \end{aligned}\right.$$

Solve the system by elimination Then state whether the system is consistent inconsistent. $$\left\\{\begin{array}{r}1.8 x+1.2 y=4 \\ 9 x+6 y=3\end{array}\right.$$

Solve the system by the method of substitution. $$\left\\{\begin{array}{l}1.5 x+0.8 y=2.3 \\ 0.3 x-0.2 y=0.1\end{array}\right.$$

Graph the solution set of the system of inequalities. $$\left\\{\begin{aligned} x+y & \leq 5 \\ x \quad & \geq 2 \\ y & \geq 0 \end{aligned}\right.$$

Solve the system of equations. $$\left\\{\begin{array}{l}4 x+3 y+5 z=10 \\ 5 x+2 y+10 z=13 \\ 3 x+y-2 z=-9\end{array}\right.$$

Solve the system by elimination Then state whether the system is consistent inconsistent. $$\left\\{\begin{array}{l}\frac{x}{4}+\frac{y}{6}=1 \\\ x-y=3\end{array}\right.$$

Solve the system by the method of substitution. $$\left\\{\begin{aligned} \frac{1}{5} x+\frac{1}{2} y &=8 \\ x+y &=20 \end{aligned}\right.$$

Graph the solution set of the system of inequalities. $$\left\\{\begin{aligned} 2 x+y & \geq 2 \\ x & \leq 2 \\ y & \leq 1 \end{aligned}\right.$$

Solve the system of equations. $$\left\\{\begin{array}{l}2 x+5 y=25 \\ 3 x-2 y+4 z=1 \\ 4 x-3 y+z=9\end{array}\right.$$

Solve the system by elimination Then state whether the system is consistent inconsistent. $$\left\\{\begin{array}{l}\frac{1}{6} x-\frac{2}{3} y=3 \\ 3 x+y=15\end{array}\right.$$

Solve the system by the method of substitution. $$\left\\{\begin{array}{l}\frac{1}{2} x+\frac{3}{4} y=10 \\ \frac{3}{2} x-y=4\end{array}\right.$$

Maximize the objective function subject to the constraints \(x+4 y \leq 20, x+y \leq 8\) \(3 x+2 y \leq 21, x \geq 0\), and \(y \geq 0\) $$z=12 x+5 y$$

Graph the solution set of the system of inequalities. $$\left\\{\begin{aligned}-3 x+2 y &<6 \\ x+4 y &<-2 \\ 2 x+y &<3 \end{aligned}\right.$$

Solve the system of equations. $$\left\\{\begin{aligned} 2 x+3 y-z &=1 \\ x-2 y+z &=7 \\ 3 x+y+2 z &=12 \end{aligned}\right.$$

Solve the system by elimination Then state whether the system is consistent inconsistent. $$\left\\{\begin{aligned} \frac{x+3}{4}+\frac{y-1}{3} &=1 \\ x-y &=3 \end{aligned}\right.$$

Solve the system by the method of substitution. $$\left\\{\begin{array}{l}6 x+5 y=-3 \\ -x-\frac{5}{6} y=-7\end{array}\right.$$

Graph the solution set of the system of inequalities. $$\left\\{\begin{array}{rr}x-7 y & >-36 \\ 5 x+2 y & >5 \\ 6 x-5 y> & 6\end{array}\right.$$

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

Solve the system by elimination Then state whether the system is consistent inconsistent. $$\left\\{\begin{array}{r}\frac{x-1}{2}+\frac{y+2}{3}=4 \\ x-2 y=5\end{array}\right.$$

Solve the system by the method of substitution. $$\left\\{\begin{array}{r}-\frac{2}{3} x+y=2 \\ 2 x-3 y=6\end{array}\right.$$

Graph the solution set of the system of inequalities. $$\left\\{\begin{array}{rr}x^{2}+y \leq & 6 \\ x \geq & -1 \\ y \geq & 0\end{array}\right.$$

Solve the system of equations. $$\left\\{\begin{array}{l}12 x+5 y+z=0 \\ 12 x+4 y-z=0\end{array}\right.$$

Solve the system by elimination Then state whether the system is consistent inconsistent. $$\left\\{\begin{aligned} 2.5 x-3 y &=1.5 \\ 10 x-12 y &=6 \end{aligned}\right.$$

Solve the system by the method of substitution. $$\left\\{\begin{array}{l}y=2 x \\ y=x^{2}-1\end{array}\right.$$