Chapter 3

Solve each system of equations by using elimination. \(1.25 x-y=-7\) \(4 y=5 x+28\)

Solve each system of equations. \(8 x-6 z=38\) \(2 x-5 y+3 z=5\) \(x+10 y-4 z=8\)

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. If the club plans to sell the canvas bags at a profit of \(\$ 20\) each and the leather bags at a profit of \(\$ 35\) each, write a function for the total profit on the bags.

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

Solve each system of equations by using substitution. \(2 j-3 k=3\) \(j+k=14\)

Solve each system of linear equations by completing a table. \(x+2 y=6\) \(2 x+y=9\)

Solve each system of inequalities by graphing. $$ \begin{array}{l}{3 x+2 y \geq 6} \\ {4 x-y \geq 2}\end{array} $$

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

Solve each system of linear equations by graphing. \(2 x+3 y=12\) \(2 x-y=4\)

Solve each system of equations. \(2 r+s+t=14\) \(-r-3 s+2 t=-2\) \(4 r-6 s+3 t=-5\)

Solve each system of inequalities by graphing. $$ \begin{array}{l}{4 x-3 y < 7} \\ {2 y-x < -6}\end{array} $$

Solve each system of equations by using substitution. \(5 a-b=17\) \(3 a+2 b=5\)

Solve each system of linear equations by graphing. \(3 x-7 y=-6\) \(x+2 y=11\)

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

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. $$ \begin{array}{l}{y \geq 1} \\ {x \leq 6} \\ {y \leq 2 x+1} \\ {f(x, y)=x+y}\end{array} $$

Solve each system of inequalities by graphing. $$ \begin{array}{l}{3 y \leq 2 x-8} \\ {y \geq \frac{2}{3} x-1}\end{array} $$

Solve each system of equations by using substitution. \(-w-z=-2\) \(4 w+5 z=16\)

Solve each system of linear equations by graphing. \(5 x-11=4 y\) \(7 x-1=8 y\)

Solve each system of equations. \(4 a-2 b+8 c=30\) \(a+2 b-7 c=-12\) \(2 a-b+4 c=15\)

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. $$ \begin{array}{l}{y \geq-4} \\ {x \leq 3} \\ {y \leq 3 x-4} \\ {f(x, y)=x-y}\end{array} $$

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

Solve each system of equations by using substitution. \(3 s+2 t=-3\) \(s+\frac{1}{3} t=-4\)

Solve each system of linear equations by graphing. \(2 x+3 y=7\) \(2 x-3 y=7\)

Solve each system of equations. \(\begin{aligned} 9 x-3 y+12 z &=39 \\ 12 x-4 y+16 z &=52 \\ 3 x-8 y+12 z &=23 \end{aligned}\)

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. $$ \begin{array}{l}{y \geq 2} \\ {1 \leq x \leq 5} \\ {y \leq x+3} \\ {f(x, y)=3 x-2 y}\end{array} $$

Solve each system of inequalities by graphing. $$ \begin{array}{l}{2 x+5 y \leq-15} \\ {y > \frac{-2}{5} x+2}\end{array} $$

Solve each system of equations by using substitution. \(2 x+4 y=6\) \(7 x=4+3 y\)

Solve each system of linear equations by graphing. \(8 x-3 y=-3\) \(4 x-2 y=-4\)

The sum of three numbers is 20. The second number is 4 times the first, and the sum of the first and third is 8. Find the numbers.

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. $$ \begin{array}{l}{y \geq 1} \\ {2 \leq x \leq 4} \\ {x-2 y \geq-4} \\ {f(x, y)=3 y+x}\end{array} $$

PART-TIME JOBS Rondell makes \(\$ 10\) an hour cutting grass and \(\$ 12\) an hour for raking leaves. He cannot work more than 15 hours per week. Graph two inequalities that Rondell can use to determine how many hours he needs to work at each job if he wants to earn at least \(\$ 120\) per week.

Solve each system of equations by using elimination. \(u+v=7\) \(2 u+v=11\)

Solve each system of linear equations by graphing. \(\frac{1}{4} x+2 y=5\) \(2 x-y=6\)

The sum of three numbers is 12. The first number is twice the sum of the second and third. The third number is 5 less than the first. Find the numbers.

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. $$ \begin{array}{l}{y \leq x+6} \\ {y+2 x \geq 6} \\ {2 \leq x \leq 6} \\\ {f(x, y)=-x+3 y}\end{array} $$

RECORDING Jane's band wants to spend no more than \(\$ 575\) recording their first \(C D\) . The studio charges at least \(\$ 35\) an hour to record. Graph a system of inequalities to represent this situation.

Solve each system of equations by using elimination. \(m-n=9\) \(7 m+n=7\)

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

In the 2004 season, Seattle’s Lauren Jackson was ranked first in the WNBA for total points and points per game. She scored 634 points making 362 shots, including 3-point field goals, 2-point field goals, and 1-point free throws. She made 26 more 2-point field goals than free throws. Write a system of equations that represents the number of goals she made.

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. $$ \begin{array}{l}{x-3 y \geq-7} \\ {5 x+y \leq 13} \\ {x+6 y \geq-9} \\ {3 x-2 y \geq-7} \\ {f(x, y)=x-y}\end{array} $$

Find the coordinates of the vertices of the figure formed by each system of inequalities. $$ \begin{array}{l}{y \geq 0} \\ {x \geq 0} \\ {x+2 y \leq 8}\end{array} $$

Solve each system of equations by using elimination. \(r+4 s=-8\) \(3 r+2 s=6\)

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. \(y=x+3\) \(y=2 x+6\)

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. $$ \begin{array}{l}{x+y \geq 4} \\ {3 x-2 y \leq 12} \\ {x-4 y \geq-16} \\\ {f(x, y)=x-2 y}\end{array} $$

Find the coordinates of the vertices of the figure formed by each system of inequalities. $$ \begin{array}{l}{y \geq-4} \\ {y \leq 2 x+2} \\ {2 x+y \leq 6}\end{array} $$

Solve each system of equations by using elimination. \(4 x-5 y=17\) \(3 x+4 y=5\)

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. \(x+y=4\) \(-4 x+y=9\)

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. $$ \begin{array}{l}{y \geq x-3} \\ {y \leq 6-2 x} \\ {2 x+y \geq-3} \\ {f(x, y)=3 x+4 y}\end{array} $$

Find the coordinates of the vertices of the figure formed by each system of inequalities. $$ \begin{array}{l}{x \leq 3} \\ {-x+3 y \leq 12} \\ {4 x+3 y \geq 12}\end{array} $$

Solve each system of equations by using elimination. \(2 c+6 d=14\) \(-\frac{7}{3}+\frac{1}{3} c=-d\)