Chapter 5

Solve each system by substitution. $$\begin{aligned}&2 x-y=6\\\&3 y=-18-x\end{aligned}$$

Solve each systen \(\begin{aligned}-3 a+5 b+c &=-4 \\ a+5 b &=3 \\ 4 a-3 c &=-11 \end{aligned}\)

Graph each equation by finding the intercepts and at least ne ether point. $$y=-3$$

Solve each system using the elimination method. $$\begin{aligned}&4+9 y=-21 x\\\&14 x+6 y=-1\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&y-4 x=-1\\\&8 x+y=2\end{aligned}$$

Write a system of equations and solve. Assume two families pay the average ticket price to attend a Green Bay Packers game in 2004 . One family buys four tickets and a parking pass for \(\$ 242.60 .\) The other family buys six tickets and a parking pass for \(\$ 351.40 .\) Find the average ticket price and the cost of a parking pass to a Packers game in 2004

Write a system of equations and solve. On vacation, Wendell buys three key chains and five postcards for \(\$ 10.00,\) and his sister buys two key chains and three postcards for \(\$ 6.50 .\) Find the cost of each souvenir.

Solve each systen \(\begin{aligned}-5 x+z &=-3 \\ 4 x-y &=-1 \\ 3 y-7 z &=1 \end{aligned}\)

Solve each system using the elimination method. $$\begin{aligned}&9 x-7 y=-14\\\&4 x+3 y=6\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&2 x-5 y=-4\\\&8 x-9 y=6\end{aligned}$$

Write a system of equations and solve. At Sparkle Car Wash, two deluxe car washes and three regular car washes would cost \(\$ 26.00 .\) Four regular washes and one deluxe wash would cost \(\$ 23.00 .\) What is the cost of a deluxe car wash and of a regular wash? (THE IMAGES CANNOT COPY)

Solve each systen \(a+b=1\) \(a-5 c=2\) \(b+2 c=-4\)

Solve each system using the elimination method. $$\begin{aligned}&6 x+5 y=13\\\&5 x+3 y=5\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&2 x+3 y=6\\\&5 x+2 y=-7\end{aligned}$$

Solve each systen \(\begin{aligned} 4 a+2 b &=-11 \\\\-8 a-3 c &=-7 \\ b+2 c &=1 \end{aligned}\)

Use the slope formula to find the slope of the line containing each pair of points. $$(1,7) \text { and }(-4,2)$$

What is the first step in solving this system by the elimination method? Do not solve. $$\begin{aligned}0.1 x+2 y &=-0.8 \\\0.03 x+0.10 y &=0.26\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&9 y-2 x=22\\\&4 x+6 y=-12\end{aligned}$$

Write a system of equations and solve. Ella spends \(\$ 7.50\) on three cantaloupe and one watermelon at a farmers' market. Two cantaloupe and two watermelon would have cost \(\$ 9.00 .\) What is the price of a cantaloupe and the price of a watermelon?

Write a system of equations and solve. One 12 -oz serving of Coke and two 12 -oz servings of Mountain Dew contain 31.3 tsp of sugar while three servings of Coke and one Mountain Dew contain 38.9 tsp of sugar. How much sugar is in a \(12-0 \mathrm{Z}\) serving of each drink? (Source; wwwdentalgentlecare com)

Solve each systen \(3 x+4 y=-6\) \(-x+3 z=1\) \(2 y+3 z=-1\)

Use the slope formula to find the slope of the line containing each pair of points. $$(-2,-3) \text { and }(3,-1)$$

What is the first step in solving this system by the elimination method? Do not solve. $$\begin{aligned}&\frac{x}{4}+\frac{y}{2}=-1\\\&\frac{3}{8} x+\frac{5}{3} y=-\frac{7}{12}\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&12 x-9 y=-8\\\&-6 x+5 y=5\end{aligned}$$

Write a system of equations and solve. Carol orders six White Castle hamburgers and a small order of fries for \(\$ 3.91,\) and Momar orders eight hamburgers and two small fries for \(\$ 5.94 .\) Find the cost of a hamburger and the cost of an order of french fries at White Castle, (Source: White Castle menu)

Solve each system \(\begin{aligned} 6 x+3 y-3 z &=-1 \\ 10 x+5 y-5 z &=4 \\ x-3 y+4 z &=6 \end{aligned}\)

Use the slope formula to find the slope of the line containing each pair of points. $$(-2,5) \text { and }(3,-8)$$

Solve each system using the elimination method. $$\begin{aligned}\frac{x}{4}+\frac{y}{2} &=-1 \\\\\frac{3}{8} x+\frac{5}{3} y &=-\frac{7}{12}\end{aligned}$$

Write a system of equations and solve. Six White Castle hamburgers and one small order of french fries contain 955 calories. Eight hamburgers and two orders of fries contain \(1350 .\) Determine how many calories are in a White Castle hamburger and in a small order of french fries. (Source: www.whitecastle com)

Solve each system \(\begin{aligned} 2 x+3 y-z &=0 \\ x-4 y-2 z &=-5 \\\\-4 x+5 y+3 z &=-4 \end{aligned}\)

Use the slope formula to find the slope of the line containing each pair of points. $$(0,4) \text { and }(8,-2)$$

Solve each system using the elimination method. $$\begin{aligned}&\frac{1}{2} x+\frac{2}{3} y=-\frac{29}{6}\\\&-\frac{1}{3} x+y=-4\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}28 x+7 y &=1 \\\4 x+y &=-6\end{aligned}$$

Write a system of equations and solve. How many ounces of a \(9 \%\) alcohol solution and how many ounces of a \(17 \%\) alcohol solution must be mixed to get 12 oz of a \(15 \%\) alcohol solution?

Solve each system \(\begin{aligned} 7 x+8 y-z &=16 \\\\-\frac{1}{2} x-2 y+\frac{3}{2} z &=1 \\\ \frac{4}{3} x+4 y-3 z &=-\frac{2}{3} \end{aligned}\)

Use the slope formula to find the slope of the line containing each pair of points. $$\left(\frac{3}{2},-1\right) \text { and }\left(-\frac{5}{2}, 7\right)$$

Solve each system using the elimination method. $$\begin{aligned}&\frac{x}{2}-\frac{y}{5}=\frac{1}{10}\\\&\frac{x}{3}+\frac{y}{4}=\frac{5}{6}\end{aligned}$$

If an equation in a system contains fractions, what should you do first to make the system easier to solve?

Write a system of equations and solve. How many milliliters of a \(4 \%\) acid solution and how many milliliters of a \(10 \%\) acid solution must be mixed to obtain \(54 \mathrm{ml}\) of a \(6 \%\) acid solution?

Solve each system \(\begin{aligned} 3 a+b-2 c &=-3 \\ 9 a+3 b-6 c &=-9 \\\\-6 a-2 b+4 c &=6 \end{aligned}\)

Use the slope formula to find the slope of the line containing each pair of points. $$(2.5,5.3) \text { and }(-3.5,-1.9)$$

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

If an equation in a system contains decimals, what should you do first to make the system easier to solve?

Solve each system \(\begin{aligned} 2 a-3 b &=-4 \\ 3 b-c &=8 \\\\-5 a+4 c &=-4 \end{aligned}\)

Use the slope formula to find the slope of the line containing each pair of points. $$(9,0) \text { and }(9,4)$$

Solve each system using the elimination method. $$\begin{aligned}x+\frac{3}{2} y &=13 \\\\-\frac{1}{8} x+\frac{1}{4} y &=\frac{1}{8}\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&\frac{1}{4} x-\frac{1}{2} y=1\\\&\frac{2}{3} x+\frac{1}{6} y=\frac{25}{6}\end{aligned}$$

\(\begin{aligned} 5 x+y-2 z &=-2 \\\\-\frac{1}{2} x-\frac{3}{4} y+2 z &=\frac{5}{4} \\ x-6 z &=3 \end{aligned}\)

Use the slope formula to find the slope of the line containing each pair of points. $$(-7,4) \text { and }(1,4)$$

Solve each system using the elimination method. $$\begin{array}{l}\frac{x}{12}-\frac{y}{6}=\frac{2}{3} \\\\\frac{x}{4}+\frac{y}{3}=2\end{array}$$