Chapter 4

Solve each system of equations by the addition method. $$ \left\\{\begin{array}{l} 3 x+y=5 \\ 6 x-y=4 \end{array}\right. $$

Solve each system of equations by the substitution method. $$ \left\\{\begin{array}{l} x+y=3 \\ x=2 y \end{array}\right. $$

The length of a rectangle is 3 feet longer than the width. The perimeter is 30 feet. Find the dimensions of the rectangle. a. length \(=8\) feet; width \(=5\) feet b. length \(=8\) feet; width \(=7\) feet c. length \(=9\) feet; width \(=6\) feet

Solve each system of equations by the addition method. $$ \left\\{\begin{array}{l} 4 x+y=13 \\ 2 x-y=5 \end{array}\right. $$

Solve each system of equations by the substitution method. $$ \left\\{\begin{array}{l} x+y=20 \\ x=3 y \end{array}\right. $$

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and \(2 .\) \(\left\\{\begin{array}{l}2 x+y=5 \\ x+3 y=5\end{array}\right.\) a. (5,0) b. (2,1)

An isosceles triangle, a triangle with two sides of equal length, has a perimeter of 20 inches. Each of the equal sides is one inch longer than the third side. Find the lengths of the three sides. a. 6 inches, 6 inches, and 7 inches b. 7 inches, 7 inches, and 6 inches c. 6 inches, 7 inches, and 8 inches

Solve each system of equations by the addition method. $$ \left\\{\begin{array}{l} x-2 y=8 \\ -x+5 y=-17 \end{array}\right. $$

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

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and \(2 .\) \(\left\\{\begin{array}{l}3 x-y=5 \\ x+2 y=11\end{array}\right.\) a. (3,4) b. (0,-5)

Two computer disks and three notebooks cost \(\$ 17\). However, five computer disks and four notebooks cost \(\$ 32\). Find the price of each. a. notebook \(=\$ 4 ;\) computer disk \(=\$ 3\) b. notebook \(=\$ 3 ;\) computer disk \(=\$ 4\) c. notebook \(=\$ 5 ;\) computer disk \(=\$ 2\)

Solve each system of equations by the addition method. $$ \left\\{\begin{array}{l} x-2 y=-11 \\ -x+5 y=23 \end{array}\right. $$

Solve each system of equations by the substitution method. $$ \left\\{\begin{array}{l} x+y=6 \\ y=-4 x \end{array}\right. $$

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and \(2 .\) \(\left\\{\begin{array}{l}2 x-3 y=8 \\ x-2 y=6\end{array}\right.\) a. (-2,-4) b. (7,2)

Two music CDs and four DVDs cost a total of \(\$ 40\). However, three music CDs and five DVDs cost \(\$ 55 .\) Find the price of each. a. \(C D=\$ 12 ; D V D=\$ 4\) b. \(C D=\$ 15 ; D V D=\$ 2\) c. \(\mathrm{CD}=\$ 10 ; \mathrm{DVD}=\$ 5\)

Solve each system of equations by the addition method. If a system contains fractions or decimals, you may want to first clear each equation of fractions or decimals. $$ \left\\{\begin{array}{l} 3 x+y=-11 \\ 6 x-2 y=-2 \end{array}\right. $$

Solve each system of equations by the substitution method. $$ \left\\{\begin{array}{l} y=3 x+1 \\ 4 y-8 x=12 \end{array}\right. $$

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and \(2 .\) \(\left\\{\begin{array}{l}2 y=4 x+6 \\ 2 x-y=-3\end{array}\right.\) a. (-3,-3) b. (0,3)

Kesha has a total of 100 coins, all of which are either dimes or quarters. The total value of the coins is \(\$ 13.00\). Find the number of each type of coin. a. 80 dimes; 20 quarters b. 20 dimes; 44 quarters c. 60 dimes; 40 quarters

Solve each system of equations by the addition method. If a system contains fractions or decimals, you may want to first clear each equation of fractions or decimals.$$ \left\\{\begin{array}{l} 4 x+y=-13 \\ 6 x-3 y=-15 \end{array}\right. $$

Solve each system of equations by the substitution method. $$ \left\\{\begin{array}{l} y=2 x+3 \\ 5 y-7 x=18 \end{array}\right. $$

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and \(2 .\) \(\left\\{\begin{array}{l}x+5 y=-4 \\ -2 x=10 y+8\end{array}\right.\) a. (-4,0) b. (6,-2)

Samuel has 28 gallons of saline solution available in two large containers at his pharmacy. One container holds three times as much as the other container. Find the capacity of each container. a. 15 gallons; 5 gallons b. 20 gallons; 8 gallons c. 21 gallons; 7 gallons

Solve each system of equations by the addition method. If a system contains fractions or decimals, you may want to first clear each equation of fractions or decimals.$$ \left\\{\begin{array}{l} 3 x+2 y=11 \\ 5 x-2 y=29 \end{array}\right. $$

Solve each system of equations by the substitution method. $$ \left\\{\begin{array}{l} y=2 x+9 \\ y=7 x+10 \end{array}\right. $$

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and \(2 .\) \(\left\\{\begin{array}{l}-2=x-7 y \\ 6 x-y=13\end{array}\right.\) a. (-2,0) b. \(\left(\frac{1}{2}, \frac{5}{14}\right)\)

Write a system of equations describing each situation. Do not solve the system. Two numbers add up to 15 and have a difference of 7 .

Solve each system of equations by the addition method. If a system contains fractions or decimals, you may want to first clear each equation of fractions or decimals.$$ \left\\{\begin{array}{l} 4 x+2 y=2 \\ 3 x-2 y=12 \end{array}\right. $$

Solve each system of equations by the substitution method. $$ \begin{array}{l} y=5 x-3 \\ y=8 x+4 \end{array} $$

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and \(2 .\) \(\left\\{\begin{array}{l}4 x=1-y \\ x-3 y=-8\end{array}\right.\) a. (0,1) b. \(\left(\frac{1}{6}, \frac{1}{3}\right)\)

Write a system of equations describing each situation. Do not solve the system. The total of two numbers is \(16 .\) The first number plus 2 more than 3 times the second equals 18 .

Solve each system of equations by the addition method. If a system contains fractions or decimals, you may want to first clear each equation of fractions or decimals.$$ \left\\{\begin{array}{l} x+5 y=18 \\ 3 x+2 y=-11 \end{array}\right. $$

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

Solve each system of linear equations by graphing. See Examples 3 through \(6 .\) \(\left\\{\begin{array}{l}x+y=4 \\ x-y=2\end{array}\right.\)

Write a system of equations describing each situation. Do not solve the system. Keiko has a total of \(\$ 6500,\) which she has invested in two accounts. The larger account has \(\$ 800\) more than the smaller account.

Solve each system of equations by the addition method. If a system contains fractions or decimals, you may want to first clear each equation of fractions or decimals.$$ \left\\{\begin{array}{l} x+4 y=14 \\ 5 x+3 y=2 \end{array}\right. $$

Solve each system of equations by the substitution method. $$ \left\\{\begin{array}{l} 4 x-3 y=10 \\ y=x-5 \end{array}\right. $$

Solve each system of linear equations by graphing. See Examples 3 through \(6 .\) \(\left\\{\begin{array}{l}x+y=3 \\ x-y=5\end{array}\right.\)

Write a system of equations describing each situation. Do not solve the system. Dominique has four times as much money in his savings account as in his checking account. The total amount is \(\$ 2300\).

Solve each system of equations by the addition method. If a system contains fractions or decimals, you may want to first clear each equation of fractions or decimals.$$ \left\\{\begin{array}{l} x+y=6 \\ x-y=6 \end{array}\right. $$

Solve eac$$ \left\\{\begin{array}{l} x+2 y=6 \\ 2 x+3 y=8 \end{array}\right. $$h system of equations by the substitution method.

Solve each system of linear equations by graphing. See Examples 3 through \(6 .\) \(\left\\{\begin{array}{l}x+y=6 \\ -x+y=-6\end{array}\right.\)

Solve. Two numbers total 83 and have a difference of 17 . Find the two numbers.

Solve each system of equations by the addition method. If a system contains fractions or decimals, you may want to first clear each equation of fractions or decimals.$$ \left\\{\begin{array}{l} x-y=1 \\ -x+2 y=0 \end{array}\right. $$

Solve each system of equations by the substitution method. $$ \left\\{\begin{array}{l} x+3 y=-5 \\ 2 x+2 y=6 \end{array}\right. $$

Solve each system of linear equations by graphing. See Examples 3 through \(6 .\) \(\left\\{\begin{array}{l}x+y=1 \\ -x+y=-3\end{array}\right.\)

Solve. The sum of two numbers is 76 and their difference is 52. Find the two numbers.

Solve each system of equations by the addition method. If a system contains fractions or decimals, you may want to first clear each equation of fractions or decimals.$$ \left\\{\begin{array}{l} 2 x+3 y=0 \\ 4 x+6 y=3 \end{array}\right. $$

Solve each system of equations by the substitution method. $$ \left\\{\begin{array}{l} 3 x+2 y=16 \\ x=3 y-2 \end{array}\right. $$

Solve each system of linear equations by graphing. See Examples 3 through \(6 .\) \(\left\\{\begin{array}{l}y=2 x \\ 3 x-y=-2\end{array}\right.\)