Chapter 4

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. $$\left\\{\begin{array}{l} x+y=-3 \\ x-y=11 \end{array}\right.$$

Determine whether the given ordered pair is a solution of the system. $$\begin{aligned}&(2,-3)\\\&\left\\{\begin{array}{l}2 x+3 y=-5 \\\7 x-3 y=23\end{array}\right.\end{aligned}$$

Let \(x\) represent one number and let \(y\) represent e he other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is \(17 .\) If one number is subtracted from the other, their difference is \(-3 .\) Find the numbers.

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

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. $$\left\\{\begin{array}{l}x+y=4 \\\y=3 x\end{array}\right.$$

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. $$\left\\{\begin{array}{l} x+y=6 \\ x-y=-2 \end{array}\right.$$

Determine whether the given ordered pair is a solution of the system. $$\begin{aligned}&(-2,-5)\\\&\left\\{\begin{array}{l}6 x-2 y=-2 \\\3 x+y=-11\end{array}\right.\end{aligned}$$

Let \(x\) represent one number and let \(y\) represent e he other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is \(5 .\) If one number is subtracted from the other, their difference is \(13 .\) Find the numbers.

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

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. $$\left\\{\begin{array}{l}x+y=6 \\\y=2 x\end{array}\right.$$.

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. $$\left\\{\begin{array}{l} 2 x+3 y=6 \\ 2 x-3 y=6 \end{array}\right.$$

Determine whether the given ordered pair is a solution of the system. $$\begin{aligned}&\left(\frac{2}{3}, \frac{1}{9}\right)\\\&\left\\{\begin{array}{r}x+3 y=1 \\\4 x+3 y=3\end{array}\right. \end{aligned}$$

Let \(x\) represent one number and let \(y\) represent e he other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. Three times a first number decreased by a second number is \(-1 .\) The first number increased by twice the second number is \(23 .\) Find the numbers.

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{rr}2 x-4 y \leq & 8 \\\x+y \geq-1\end{array}\right.$$

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. $$\left\\{\begin{array}{l}x+3 y=8 \\\y=2 x-9\end{array}\right.$$

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. $$\left\\{\begin{array}{l} 3 x+2 y=14 \\ 3 x-2 y=10 \end{array}\right.$$

Determine whether the given ordered pair is a solution of the system. $$\begin{aligned}&\left(\frac{7}{25},-\frac{1}{25}\right)\\\&\left\\{\begin{array}{l}4 x+3 y=1 \\\3 x-4 y=1\end{array}\right. \end{aligned}$$

Let \(x\) represent one number and let \(y\) represent e he other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of three times a first number and twice a second number is \(43 .\) If the second number is subtracted from twice the first number, the result is \(-4 .\) Find the numbers.

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{c}4 x+3 y \leq 12 \\\x-2 y \leq 4\end{array}\right.$$

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. $$\left\\{\begin{array}{l}2 x-3 y=-13 \\\y=2 x+7\end{array}\right.$$

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. $$\left\\{\begin{array}{r} x+2 y=7 \\ -x+3 y=18 \end{array}\right.$$

Determine whether the given ordered pair is a solution of the system. $$\begin{aligned}&(-5,9)\\\&\left\\{\begin{aligned}5 x+3 y &=2 \\\x+4 y &=14\end{aligned}\right.\end{aligned}$$

The bar graph shows the average time per day that Americans devote to sprucing up. (GRAPH CAN NOT COPY) Each day, the sum of the average times spent on grooming for 20 - to 24 -year- old women and men is 86 minutes. The difference between grooming times for 20 - to 24 -year-old women and men is 12 minutes. How many minutes per day do 20 - to 24 -year-old women and men spend on grooming?

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x+3 y \leq 6 \\\x-2 y \leq 4\end{array}\right.$$

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. $$\left\\{\begin{array}{l}x+3 y=5 \\\4 x+5 y=13\end{array}\right.$$

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. $$\left\\{\begin{array}{l} 2 x+y=-2 \\ -2 x-3 y=-6 \end{array}\right.$$

Determine whether the given ordered pair is a solution of the system. $$\begin{aligned}&(10,7)\\\&\left\\{\begin{array}{l}6 x-5 y=25 \\\4 x+15 y=13\end{array}\right.\end{aligned}$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}2 x+y \leq 4 \\\2 x-y \leq 6\end{array}\right.$$

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. $$\left\\{\begin{array}{l}x+2 y=5 \\\2 x-y=-15\end{array}\right.$$

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. $$\left\\{\begin{aligned} 5 x-y &=x 14 \\ -5 x+2 y &=-13 \end{aligned}\right.$$

Determine whether the given ordered pair is a solution of the system. $$\begin{aligned}&(1400,450)\\\&\left\\{\begin{array}{r}x-2 y=500 \\\0.03 x+0.02 y=51\end{array}\right.\end{aligned}$$

It's probably not a good idea if you want to look like Mr. Universe or Kate Winslet. The graph shows the four candy bars with the highest fat content, representing grams of fat and calories in each bar. (GRAPH CAN NOT COPY) One Mr. Goodbar and two Mounds bars contain 780 calories. Two Mr. Goodbars and one Mounds bar contain 786 calories. Find the caloric content of each candy bar.

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{r}x-2 y>4 \\\2 x+y \geq 6\end{array}\right.$$

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. $$\left\\{\begin{array}{l}2 x-y=-5 \\\x+5 y=14\end{array}\right.$$

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. $$\left\\{\begin{array}{rr} 7 x-4 y= & 13 \\ -7 x+6 y= & -11 \end{array}\right.$$

Determine whether the given ordered pair is a solution of the system. $$\begin{aligned}&(8,5)\\\&\left\\{\begin{aligned}5 x-4 y &=20 \\\3 y &=2 x+1\end{aligned}\right.\end{aligned}$$

It's probably not a good idea if you want to look like Mr. Universe or Kate Winslet. The graph shows the four candy bars with the highest fat content, representing grams of fat and calories in each bar. (GRAPH CAN NOT COPY) One Snickers bar and two Reese's Peanut Butter Cups contain 737 calories. Two Snickers bars and one Reese's Peanut Butter Cup contain 778 calories. Find the caloric content of each candy bar.

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{c}3 x+y<6 \\\x+2 y \geq 2\end{array}\right.$$

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. $$\left\\{\begin{array}{l}2 x+3 y=11 \\\x-4 y=0\end{array}\right.$$

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. $$\left\\{\begin{array}{r} 3 x+y=7 \\ 2 x-5 y=-1 \end{array}\right.$$

Determine whether the given ordered pair is a solution of the system. $$\begin{aligned}&(8,5)\\\&\left\\{\begin{aligned}5 x-4 y &=20 \\\3 y &=2 x+1\end{aligned}\right.\end{aligned}$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x+y>1 \\\x+y<4\end{array}\right.$$

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. $$\left\\{\begin{array}{l}2 x-y=3 \\\5 x-2 y=10\end{array}\right.$$

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. $$\left\\{\begin{array}{l} 3 x-y=11 \\ 2 x+5 y=13 \end{array}\right.$$

Determine whether the given ordered pair is a solution of the system. $$\begin{aligned}&(5,-2)\\\&\left\\{\begin{aligned}4 x-3 y &=26 \\\x &=15-5 y\end{aligned}\right.\end{aligned}$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x-y>1 \\\x-y<3\end{array}\right.$$

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. $$\left\\{\begin{array}{l}-3 x+y=-1 \\\x-2 y=4\end{array}\right.$$

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. $$\left\\{\begin{array}{r} x+3 y=4 \\ 4 x+5 y=2 \end{array}\right.$$

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. $$\left\\{\begin{array}{l}x+y=6 \\\x-y=2\end{array}\right.$$

In a discount clothing store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. If one sweater and three shirts cost 42 dollar while three sweaters and two shirts cost 56 dollar find the price of one sweater and the price of one shirt.