Chapter 4

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}2(x-1)-y=-3 \\\y=2 x+3\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x \leq 3 \\\y \geq-2\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 9 x=25+y \\ 2 y=4-9 x \end{array}\right.$$

On a special day, tickets for a minor league baseball game cost 5 dollar for adults and 1 dollar for students. The attendance that day was 1281 and 3425 dollar was collected. Find the number of each type of ticket sold.

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=2 x+1 \\ y=-2 x-3\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}x+y-1=2(y-x) \\\y=3 x-1\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x \leq 4 \\\y \leq-3\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 2 x=3 y-4 \\ -6 x+12 y=6 \end{array}\right.$$

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=-2 x+3 \\ y=-x+1\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}x=2 y+9 \\\x=7 y+10\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x \geq 3 \\\y<2\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 5 x=4 y-8 \\ 3 x+7 y=14 \end{array}\right.$$

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=3 x-4 \\ y=-2 x+1\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}x=5 y-3 \\\x=8 y+4\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x \geq-2 \\\y<-1\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 2 x-y=3 \\ 4 x+4 y=-1 \end{array}\right.$$

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=2 x-1 \\ y=2 x+1\end{array}\right.$$

Solve each system by the substinuion method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets.$ $$\left\\{\begin{array}{l}4 x-y=100 \\\0.05 x-0.06 y=-32\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x \geq 0 \\\y \leq 0\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{rr} 3 x-y= & 22 \\ 4 x+5 y= & -21 \end{array}\right.$$

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=3 x-1 \\ y=3 x+2\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}4 x-y=100 \\\0.05 x-0.06 y=-32\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x \leq 0 \\\y \geq 0\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 4 x=5+2 y \\ 2 x+3 y=4 \end{array}\right.$$

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}x+y=4 \\ x=-2\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=\frac{1}{3} x+\frac{2}{3} \\\y=\frac{5}{7} x-2\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x \geq 0 \\\y>0\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 3 x=4 y+1 \\ 4 x+3 y=1 \end{array}\right.$$

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}x+y=6 \\ y=-3\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=-\frac{1}{2} x+2 \\\y=\frac{3}{4} x+7\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x \leq 0 \\\y<0\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 3 x-y=1 \\ 3 x-y=2 \end{array}\right.$$

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}x-2 y=4 \\ 2 x-4 y=8\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$ \left\\{\begin{array}{l} \frac{x}{6}-\frac{y}{2}=\frac{1}{3} \\ x+2 y=-3 \end{array}\right. $$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x+y \leq 5 \\\x \geq 0 \\\y \geq 0\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{aligned} 4 x-9 y &=-2 \\ -4 x+9 y &=-2 \end{aligned}\right.$$

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}2 x+3 y=6 \\ 4 x+6 y=12\end{array}\right.$$

Solve each system by the substinuion method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets.$ $$\left\\{\begin{array}{l}\frac{x}{4}-\frac{y}{4}=-1 \\\x+4 y=-9\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$ \left\\{\begin{array}{l} \frac{x}{4}-\frac{y}{4}=-1 \\ x+4 y=-9 \end{array}\right. $$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}2 x+y \leq 4 \\\x \geq 0 \\\y \geq 0\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{r} x+3 y=2 \\ 3 x+9 y=6 \end{array}\right.$$

Involve dual investments. A bank loaned out 120,000 dollar part of it at the rate of \(8 \%\) annual mortgage interest and the rest at the rate of \(18 \%\) annual credit card interest. The interest received on both loans totaled 10,000 dollar How much was loaned at each rate? Organize your work in the following table. (TABLE CAN NOT COPY))

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=2 x-1 \\ x-2 y=-4\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}2 x-3 y=8-2 x \\\3 x+4 y=x+3 y+14\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}4 x-3 y>12 \\\x \geq 0 \\\y \leq 0\end{array}\right.$$

Involve dual investments. A bank loaned out 250,000 dollar, part of it at the rate of \(8 \%\) annual mortgage interest and the rest at the rate of \(18 \%\) annual credit card interest. The interest received on both loans totaled 23,000 dollar How much was loaned at each rate? Organize your work in the following table. (TABLE CAN NOT COPY)

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 4 x-2 y=2 \\ 2 x-y=1 \end{array}\right.$$

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=-2 x-4 \\ 4 x-2 y=8\end{array}\right.$$

Solve each system by the substinuion method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}3 x-4 y=x-y+4 \\\2 x+6 y=5 y-4\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}2 x-6 y>12 \\\x \leq 0 \\\y \leq 0\end{array}\right.$$