Chapter 3

Solve each system of equations. \(x+2 y=12\) \(3 y-4 z=25\) \(x+6 y+z=20\)

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region. $$ \begin{array}{l}{y \geq 2} \\ {x \geq 1} \\ {x+2 y \leq 9} \\ {f(x, y)=2 x-3 y}\end{array} $$

Solve each system of inequalities by graphing. $$ \begin{array}{l}{x \leq 4} \\ {y > 2}\end{array} $$

Solve each system of equations by using substitution. \(y=3 x-4\) \(y=4+x\)

Solve each system of equations by completing a table. \(y=2 x+9\) \(y=-x+3\)

Solve each system of equations. \(9 a+7 b=-30\) \(8 b+5 c=11\) \(-3 a+10 c=73\)

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region. $$ \begin{array}{l}{y \leq 2 x+1} \\ {1 \leq y \leq 3} \\ {x+2 y \leq 12} \\\ {f(x, y)=3 x+y}\end{array} $$

Solve each system of inequalities by graphing. $$ \begin{array}{l}{y \leq-4 x-3} \\ {y>-4 x+1}\end{array} $$

Solve each system of equations by using substitution. \(4 c+2 d=10\) \(c+3 d=10\)

Solve each system of equations by completing a table. \(3 x+2 y=10\) \(2 x+3 y=10\)

Solve each system of equations. \(r-3 s+t=4\) \(3 r-6 s+9 t=5\) \(4 r-9 s+10 t=9\)

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region. $$ \begin{array}{l}{x \leq 5} \\ {y \geq-2} \\ {y \leq x-1} \\ {f(x, y)=x-2 y}\end{array} $$

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

Solve each system of equations by using substitution. \(a-b=2\) \(-2 a+3 b=3\)

Solve each system of equations by graphing. \(4 x-2 y=22\) \(6 x+9 y=-3\)

Solve each system of equations. \(2 r+3 s-4 t=20\) \(4 r-s+5 t=13\) \(3 r+2 s+4 t=15\)

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region. $$ \begin{array}{l}{y \geq-x+3} \\ {1 \leq x \leq 4} \\ {y \leq x+4} \\ {f(x, y)=-x+4 y}\end{array} $$

Solve each system of inequalities by graphing. $$ \begin{array}{l}{y \geq 3 x+3} \\ {y < 3 x-2}\end{array} $$

Solve each system of equations by using substitution. \(3 g-2 h=-1\) \(4 g+h=17\)

Solve each system of equations by graphing. \(y=2 x-4\) \(y=-3 x+1\)

Solve each system of equations. \(2 x-y+z=1\) \(x+2 y-4 z=3\) \(4 x+3 y-7 z=-8\)

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region. $$ \begin{array}{l}{y \geq-x+2} \\ {2 \leq x \leq 7} \\ {y \leq \frac{1}{2} x+5} \\ {f(x, y)=8 x+3 y}\end{array} $$

SHOPPING For Exercises 5 and \(6,\) use the following information. The most Jack can spend on bagels and muffins for the cross country team is \(\$ 28 .\) A package of 6 bagels costs \(\$ 2.50 .\) A package of muffins costs \(\$ 3.50\) and contains 8 muffins. He needs to buy at least 12 bagels and 24 muffins. Graph the region that shows how many packages of each item he can purchase.

Campus Rentals rents 2- and 3-bedroom apartments for \(\$ 700\) and \(\$ 900\) per month, respectively. Last month they had six vacant apartments and reported \(\$ 4600\) in lost rent. How many 2-bedroom apartments were vacant? A. 2 B. 3 C. 4 D. 5

Developing Digital Photos EZ Online Digital Photos Charges \(\$ 0.15\) per digital photo and \(\$ 2.70\) for shipping Local Pharmacy Charges \(\$ 0.25\) per digital photo Write equations that represent the cost of printing digital photos at each lab.

Solve each system of equations. \(x+y+z=12\) \(6 x-2 y-z=16\) \(3 x+4 y+2 z=28\)

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region. $$ \begin{array}{l}{x+2 y \leq 6} \\ {2 x-y \leq 7} \\ {x \geq-2, y \geq-3}\end{array} $$

SHOPPING For Exercises 5 and \(6,\) use the following information. The most Jack can spend on bagels and muffins for the cross country team is \(\$ 28 .\) A package of 6 bagels costs \(\$ 2.50 .\) A package of muffins costs \(\$ 3.50\) and contains 8 muffins. He needs to buy at least 12 bagels and 24 muffins. Give an example of three different purchases he can make.

Solve each system of equations by using elimination. \(2 r-3 s=11\) \(2 r+2 s=6\)

Developing Digital Photos EZ Online Digital Photos Charges \(\$ 0.15\) per digital photo and \(\$ 2.70\) for shipping Local Pharmacy Charges \(\$ 0.25\) per digital photo Under what conditions is the cost to print digital photos the same for either store?

Jambalaya is a Cajun dish made from chicken, sausage, and rice. Simone is making a large pot of of jambalaya for a party. Chicken costs \(\$ 6\) per pound, sausage costs \(\$ 3\) per pound, and rice costs \(\$ 1\) per pound. She spends \(\$ 42\) on 13.5 pounds of food. She buys twice as much rice as sausage. Write a system of three equations that represents how much food Simone purchased.

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region. $$ \begin{array}{l}{x \geq-3} \\ {y \leq 1} \\ {3 x+y \leq 6} \\ {f(x, y)=5 x-2 y}\end{array} $$

Find the coordinates of the vertices of the figure formed by each system of inequalities. $$ \begin{array}{l}{y \leq x} \\ {y \geq-3} \\ {3 y+5 x \leq 16}\end{array} $$

Solve each system of equations by using elimination. \(5 m+n=10\) \(4 m+n=4\)

Developing Digital Photos EZ Online Digital Photos Charges \(\$ 0.15\) per digital photo and \(\$ 2.70\) for shipping Local Pharmacy Charges \(\$ 0.25\) per digital photo When is it best to use EZ Online Digital Photos and when is it best to use the local pharmacy?

Jambalaya is a Cajun dish made from chicken, sausage, and rice. Simone is making a large pot of of jambalaya for a party. Chicken costs \(\$ 6\) per pound, sausage costs \(\$ 3\) per pound, and rice costs \(\$ 1\) per pound. She spends \(\$ 42\) on 13.5 pounds of food. She buys twice as much rice as sausage. How much chicken, sausage, and rice will she use in her dish?

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region. $$ \begin{array}{l}{y \leq x+2} \\ {y \leq 11-2 x} \\ {2 x+y \geq-7} \\ {f(x, y)=4 x-3 y}\end{array} $$

Find the coordinates of the vertices of the figure formed by each system of inequalities. $$ \begin{array}{l}{y \geq x-3} \\ {y \leq x+7} \\ {x+y \leq 11} \\ {x+y \geq-1}\end{array} $$

Solve each system of equations by using elimination. \(2 p+4 q=18\) \(3 p-6 q=3\)

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. \(y=6-x\) \(y=x+4\)

Solve each system of equations. \(2 x-y=2\) \(3 z=21\) \(4 x+z=19\)

For Exercises \(9-14,\) use the following information. The Future Homemakers Club is making canvas tote bags and leather tote bags for a fund-raiser. They will line both types of tote bags with canvas and use leather for the handles of both. For the canvas bags, they need 4 yards of canvas and 1 yard of leather. For the leather bags, they need 3 yards of leather and 2 yards of canvas. Their advisor purchased 56 yards of leather and 104 yards of canvas. Let c represent the number of canvas bags and let \(\ell\) represent the number of leather bags. Write a system of inequalities for the number of bags that can be made.

Solve each system of inequalities by graphing. $$ \begin{array}{l}{x \geq 2} \\ {y > 3}\end{array} $$

Solve each system of equations by using elimination. \(\frac{1}{4} x+y=\frac{11}{4}\) \(x-\frac{1}{2} y=2\)

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. \(x+2 y=2\) \(2 x+4 y=8\)

For Exercises \(9-14,\) use the following information. The Future Homemakers Club is making canvas tote bags and leather tote bags for a fund-raiser. They will line both types of tote bags with canvas and use leather for the handles of both. For the canvas bags, they need 4 yards of canvas and 1 yard of leather. For the leather bags, they need 3 yards of leather and 2 yards of canvas. Their advisor purchased 56 yards of leather and 104 yards of canvas. Draw the graph showing the feasible region.

Solve each system of inequalities by graphing. $$ \begin{array}{l}{x \leq-1} \\ {y \geq-4}\end{array} $$

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. \(x-2 y=8\) \(\frac{1}{2} x-y=4\)

Solve each system of equations. \(5 x+2 y=4\) \(3 x+4 y+2 z=6\) \(7 x+3 y+4 z=29\)

Solve each system of inequalities by graphing. $$ \begin{array}{l}{y < 2-x} \\ {y > x+4}\end{array} $$