Exam 4: Solving Systems of Linear Equations

Fill in the blank with one of the words or phrases listed below. system of linear equations solution consistent independent dependent inconsistent substitution addition -In a system of linear equations in two variables, if the graphs of the equations are the same, the equations are equations.

Solve the system. - $\left\{ \begin{array} { l } 2 x + 5 y + z = - 18 \\3 x - 3 y - z = 23 \\3 x + y + 4 z = 8\end{array} \right.$

Solve. -One number is four more than a second number. Two times the first number is 8 more than four times the second number.

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

Determine whether the ordered pair is a solution of the system of linear equations. - (2,6); 3x=0-y 4x=10-3y

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

Solve. -Two numbers total 8, and their difference is 20. Find the two numbers.

Solve. -The manager of a bulk foods establishment sells a trail mix for $6 per pound and premium cashews for $10 per pound. The manager wishes to make a 200-pound trail mix-cashew mixture that will Sell for $7 per pound. How many pounds of each should be used?

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + 4 y = - 7 \\9 x + 3 y = 36\end{array} \right.$

Determine whether the ordered pair is a solution of the system of linear equations. - (-4,-5); x+y=-1 x-y=9

Write a system of equations in x and y describing the situation. Do not solve the system. -Bowie has $\$ 11$ less in his pocket than Donna has. If Donna had $\$ 5$ more, she would have 3 times as much money as Bowie.

Fill in the blank with one of the words or phrases listed below. system of linear equations solution consistent independent dependent inconsistent substitution addition -A system of equations that has no solution is called a(n) system.

Determine whether the ordered pair is a solution of the system of linear equations. - $(-6,-3)$ $\left\{ \begin{array} { l } 4 x + y = - 27 \\3 x + 4 y = - 30\end{array} \right.$

Solve. -A store sells tents, sleeping bags, and camp stools. A customer buys a tent, 3 sleeping bags, and 3 camp stools for $220. The price of the tent is 7 times the cost of a camp stool. The cost of a sleeping Bag is $30 more than the cost of a camp stool. Find the cost of each item.

Fill in the blank with one of the words or phrases listed below. system of linear equations solution consistent independent dependent inconsistent substitution addition -A(n) of a system of two equations in two variables is an ordered pair of numbers that is a solution of both equations in the system.

Solve. -Natasha rides her bike (at a constant speed) for 4 hours, helped by a wind of 2 miles per hour. Pedaling at the same rate, the trip back against the wind takes 8 hours. Find find the total round trip distance she traveled.

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } y = 1.1 x + 3.7 \\y = 0.7 x + 0.98\end{array} \right.$

Solve the problem by writing and using a system of linear equations. -Two bikers start at opposite ends of a trail and bike toward each other. The trail is 150 miles long and they meet in 5 hours. If one biker is twice as fast as the other, find both biking speeds.

Solve the system. - $\left\{ \begin{aligned}x + 2 y + 4 z & = 0 \\5 y + 3 z & = 9 \\z & = - 2\end{aligned} \right.$

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -Use the revenue and cost functions to write the profit function from producing and selling x binoculars.