Chapter 5

Determine if the ordered triple is a solution of the system. \(\begin{aligned} 4 x+3 y-7 z &=-6 \\ x-2 y+5 z &=-3 \\\\-x+y+2 z &=7 \\\\(-2,3,1) & \end{aligned}\)

Write a system of equations and solve. The sum of two numbers is \(36,\) and one number is two more than the other. Find the numbers.

Solve each system using the elimination method. $$\begin{aligned}&x-3 y=1\\\&-x+y=-3\end{aligned}$$

(4.1) Determine if each ordered pair is a solution of the given equation. $$4 x-y=9 ;(1,-5)$$

If you were asked to solve this system by substitution, why would it be easiest to begin by solving for y in the second equation? $$\begin{array}{c}6 x-2 y=-5 \\\3 x+y=4\end{array}$$

Determine if the ordered triple is a solution of the system. \(3 x+y+2 z=2\) \(-2 x-y+z=5\) \(x+2 y-z=-11\) \((1,-5,2)\)

Write a system of equations and solve. One number is half another number. The sum of the two numbers is \(108 .\) Find the numbers.

Solve each system using the elimination method. $$\begin{array}{r}-2 x-y=-1 \\\4 x+y=-5\end{array}$$

When solving a system by substitution, how do you know if the system has. a) no solution? b) an infinite number of solutions?

(4.1) Determine if each ordered pair is a solution of the given equation. $$3 x+2 y=20 ;(-4,2)$$

Determine if the ordered triple is a solution of the system. \(-x+y-2 z=2\) \(3 x-y+5 z=4\) \(2 x+3 y-z=7\) \((0,6,2)\)

Write a system of equations and solve. In \(2005,\) The Aviator was nominated for four more Academy Awards than the movie Finding Neverland. Together they received 18 nominations. How many Academy Award nominations did each movie receive? (Source; Chicago Tribune, \(1 / 26 / 05\) )

Solve each system using the elimination method. $$\begin{aligned}&3 x+5 y=-10\\\&7 x-5 y=10\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&y=3 x+4\\\&-6 x+y=-2\end{aligned}$$

(4.1) Determine if each ordered pair is a solution of the given equation. $$y=\frac{5}{4} x+\frac{1}{2} ;(2,3)$$

Determine if the ordered triple is a solution of the system. \(6 x-y+4 z=4\) \(-2 x+y-z=5\) \(2 x-3 y+z=2\) \(\left(-\frac{1}{2},-3,1\right)\)

Write a system of equations and solve. Through \(2005,\) the University of Southern California football team played in 10 more Rose Bowl games than the University of Michigan. All together, these teams have appeared in 48 Rose Bowls. How many appearances did each team make in the Rose Bowl? (Source: www tournamentofroses com)

Solve each system using the elimination method. $$\begin{aligned}4 x-3 y &=-5 \\\\-4 x+5 y &=11\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&3 x+y=15\\\&y=4 x-6\end{aligned}$$

(4.1) Determine if each ordered pair is a solution of the given equation. $$x=7 ;(7,-9)$$

Solve each system. \begin{aligned} x+3 y+z &=3 \\ 4 x-2 y+3 z &=7 \\ -2 x+y-z &=-1 \end{aligned}

Write a system of equations and solve. There were a total of 2626 IHOP and Waffle House restaurants across the United States at the end of 2004\. There were 314 fewer IHOPs than Waffle Houses. Determine the number of IHOP and Waffle House restaurants in the United States. (Source; www.thop.com, www ajc com)

Solve each system using the elimination method. $$\begin{aligned}&7 x+6 y=3\\\&3 x+2 y=-1\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&2 x-y=5\\\&x=y+6\end{aligned}$$

Complete the ordered pair for each equation. $$y=-6 x+10 ;(-3,)$$

Solve each system. \begin{aligned} x-y+2 z &=-7 \\ -3 x-2 y+z &=-10 \\ 5 x+4 y+3 z &=4 \end{aligned}

Write a system of equations and solve. Through \(2004,\) the University of Kentucky men's basketball team won four fewer NCAA championships than UCLA. The two teams won a total of 18 championship titles. How many championships did each team win? (Source: www.ncaasports com)

Solve each system using the elimination method. $$\begin{array}{c}-8 x+5 y=-16 \\\4 x-7 y=8\end{array}$$

Solve each system by substitution. $$\begin{aligned}&x=y-8\\\&-3 x-y=12\end{aligned}$$

Complete the ordered pair for each equation. $$y=\frac{2}{3} x+5 ;(12,)$$

\begin{aligned} -2 x-2 y+3 z &=2 \\ 3 x+3 y-5 z &=-3 \\ -x+y-z &=9 \end{aligned}

Write a system of equations and solve. The first NCAA Men's Basketball Championship game was played in 1939 in Evanston, Illinois. In\(2004,38,968\) more people attended the final game in San Antonio than attended the first game in Evanston. The total number of people who attended these two games was \(49,968 .\) How many people saw the first NCAA championship in \(1939,\) and how many were at the game in \(2004 ?\) (Source: www neassports, com)

Solve each system using the elimination method. $$\begin{aligned}3 x-y &=4 \\\\-6 x+2 y &=-8\end{aligned}$$

Solve each system by substitution. $$\begin{array}{r}2 x+5 y=8 \\\x-6 y=4\end{array}$$

Complete the ordered pair for each equation. $$y=-8 ;(5,)$$

\begin{aligned} -2 x-2 y+3 z &=2 \\ 3 x+3 y-5 z &=-3 \\ -x+y-z &=9 \end{aligned}

Write a system of equations and solve. Garth Brooks won two more Country Music Awards than Tim McGraw through 2004 . They won a total of 20 awards. How many awards did each man win? (Source: www cmaawards com)

Solve each system using the elimination method. $$\begin{aligned}5 x-6 y &=-2 \\\10 x-12 y &=7\end{aligned}$$

Solve each system by substitution. $$\begin{array}{c}x+3 y=-12 \\\3 x+4 y=-6\end{array}$$

Complete the ordered pair for each equation. $$5 x-9 y=3 ;(,-2)$$

\begin{aligned} 3 a+5 b-3 c &=-4 \\ a-3 b+c &=6 \\ -4 a+6 b+2 c &=-6 \end{aligned}

Write a system of equations and solve. Annual per capita consumption of chicken in the United States in 2001 was 6.3 lb less than that of beef. Together, each American consumed, on average, 120.5 Ib of beef and chicken in 2001 . Find the amount of beef and the amount of chicken consumed, per person, in 2001 . (Source: US. Department of Agriculture)

Solve each system using the elimination method. $$\begin{aligned}&3 x+2 y=-9\\\&2 x-7 y=19\end{aligned}$$

Complete the table of values for each equation. $$y=x-11$$

Solve each system by substitution. $$\begin{aligned}&2 x+30 y=9\\\&x=6-15 y\end{aligned}$$

Solve each systen \begin{aligned} a-4 b+2 c &=-7 \\ 3 a-8 b+c &=7 \\ 6 a-12 b+3 c &=12 \end{aligned}

Write a system of equations and solve. Mr. Chen has 27 students in his American History class. For their assignment on the Civil War, twice as many students chose to give a speech as chose to write a paper. How many students will be giving speeches, and how many will be writing papers?

Solve each system using the elimination method. $$\begin{array}{c}3 x-5 y=-1 \\\\-4 x+7 y=2\end{array}$$

Solve each system by substitution. $$\begin{aligned}&y=-3 x-20\\\&6 x+2 y=5\end{aligned}$$

Solve each systen \begin{aligned} a-5 b+c &=-4 \\ 3 a+2 b-4 c &=-3 \\ 6 a+4 b-8 c &=9 \end{aligned}