Without solving the following system of equations, tell what the solution is. Explain your answer. \[\begin{aligned} 3 x-6 y-3 z & =2 \\ -18 x+36 y+18 z & =-12 \\ 3 x-3 y-2 z & =-5 \end{aligned}\]

There are an infinite numbers of solutio

Exam 4: Systems of Linear Equations

The graphs below represent the supply and demand for a product at various prices per unit. Approximately how many units should be produced so that supply equals demand?

(Multiple Choice)

4.8/5

(34)

Question 61

A woman made a deposit of $\$ 260$ . If her deposit consisted of 100 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

(Multiple Choice)

4.9/5

(34)

Question 62

Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 23 coins with a total face value of $\$ 4.55$ , how many of the coins are nickels?

(Multiple Choice)

4.8/5

(44)

Question 63

Tell how many solutions the system has. Do not actually solve. - $2 x-y=5$ $-4 x+2 y=-18$

(Multiple Choice)

5.0/5

(37)

Question 64

What is the graph of an equation in three variables?

(Multiple Choice)

4.9/5

(32)

Question 65

$x+y+z=7$ $x-y+2 z=7$ $5 \mathrm{x}+\mathrm{y}+\mathrm{z}=11$

(Multiple Choice)

4.9/5

(32)

Question 66

Anne and Nancy use a metal alloy that is $19 \%$ copper to make jewelry. How many ounces of an alloy that is $12 \%$ copper must be mixed with an alloy that is $25 \%$ copper to form 65 ounces of the desired alloy?

(Multiple Choice)

4.9/5

(29)

Question 67

Without solving the following system of equations, tell what the solution is. Explain your answer. 3x-6y-3z =2 -18x+36y+18z =-12 3x-3y-2z =-5

(Essay)

4.8/5

(37)

Question 68

Solve the problem using a system of equations. -Anne and Nancy use a metal alloy that is $18.4 \%$ copper to make jewelry. How many ounces of a $17 \%$ alloy must be mixed with a $19 \%$ alloy to form 110 ounces of the desired alloy?

(Multiple Choice)

4.7/5

(37)

Question 69

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $x-3 y=-3$ $7 \mathrm{x}-2 \mathrm{y}=-21$

(Multiple Choice)

4.7/5

(36)

Question 70

Decide whether the ordered pair is a solution of the given system - $x+y=7$ $\mathrm{x}-\mathrm{y}=3 ;(-5,2)$

(True/False)

4.8/5

(35)

Question 71

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $y=13-6 x$ $x+6 y=-27$

(Multiple Choice)

4.8/5

(28)

Question 72

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $-7 x+9 y=-42$ $-5 x+2 y=-30$

(Multiple Choice)

4.8/5

(34)

Question 73

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - x-y+2z=2 5x+z=0 x+4y+z=-8

(Multiple Choice)

4.9/5

(32)

Question 74

Solve the problem using a system of equations. -Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 90.00$ for 3 days and 300 miles, while Mary was charged $\$ 160.00$ for 5 days and 600 miles. What does Best Rentals charge per day and per mile?

(Multiple Choice)

4.9/5

(44)

Question 75

The table shown was generated by a graphing calculator. The functions defined by $y_{1}$ and y2 are linear. Based on the table, solve the system of equations formed by $\mathrm{y}_{1}$ and $\mathrm{y}_{2}$ . $The table shown was generated by a graphing calculator. The functions defined by y_{1} and y2 are linear. Based on the table, solve the system of equations formed by \mathrm{y}_{1} and \mathrm{y}_{2} .$

(Multiple Choice)

4.8/5

(39)

Question 76

The side of an equilateral triangle is 3 inches shorter than the side of a square. The perimeter of the square is 37 inches more than the perimeter of the triangle. Find the length of a side of the square.

(Multiple Choice)

4.8/5

(22)

Question 77

A cruise boat travels 36 miles downstream in 3 hours and returns to its starting point upstream in 6 hours. Find the speed of the stream.

(Multiple Choice)

4.9/5

(31)

Question 78

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $x-3 y=3$ $x=8+3 y$

(Multiple Choice)

4.9/5

(28)

Question 79

Ellen wishes to mix candy worth $\$ 2.12$ per pound with candy worth $\$ 3.71$ per pound to form 26 pounds of a mixture worth $\$ 2.73$ per pound. How many pounds of the more expensive candy should she use?

(Multiple Choice)

4.9/5

(33)

Question 80

The graphs below represent the supply and demand for a product at various prices per unit. Approximately how many units should be produced so that supply equals demand?

A woman made a deposit of $\$ 260$ . If her deposit consisted of 100 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 23 coins with a total face value of $\$ 4.55$ , how many of the coins are nickels?

Tell how many solutions the system has. Do not actually solve. - $2 x-y=5$ $-4 x+2 y=-18$

What is the graph of an equation in three variables?

$x+y+z=7$ $x-y+2 z=7$ $5 \mathrm{x}+\mathrm{y}+\mathrm{z}=11$

Anne and Nancy use a metal alloy that is $19 \%$ copper to make jewelry. How many ounces of an alloy that is $12 \%$ copper must be mixed with an alloy that is $25 \%$ copper to form 65 ounces of the desired alloy?

Without solving the following system of equations, tell what the solution is. Explain your answer. 3x-6y-3z =2 -18x+36y+18z =-12 3x-3y-2z =-5

Solve the problem using a system of equations. -Anne and Nancy use a metal alloy that is $18.4 \%$ copper to make jewelry. How many ounces of a $17 \%$ alloy must be mixed with a $19 \%$ alloy to form 110 ounces of the desired alloy?

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $x-3 y=-3$ $7 \mathrm{x}-2 \mathrm{y}=-21$

Decide whether the ordered pair is a solution of the given system - $x+y=7$ $\mathrm{x}-\mathrm{y}=3 ;(-5,2)$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $y=13-6 x$ $x+6 y=-27$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $-7 x+9 y=-42$ $-5 x+2 y=-30$

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - x-y+2z=2 5x+z=0 x+4y+z=-8

Solve the problem using a system of equations. -Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 90.00$ for 3 days and 300 miles, while Mary was charged $\$ 160.00$ for 5 days and 600 miles. What does Best Rentals charge per day and per mile?

The side of an equilateral triangle is 3 inches shorter than the side of a square. The perimeter of the square is 37 inches more than the perimeter of the triangle. Find the length of a side of the square.

A cruise boat travels 36 miles downstream in 3 hours and returns to its starting point upstream in 6 hours. Find the speed of the stream.

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $x-3 y=3$ $x=8+3 y$

Ellen wishes to mix candy worth $\$ 2.12$ per pound with candy worth $\$ 3.71$ per pound to form 26 pounds of a mixture worth $\$ 2.73$ per pound. How many pounds of the more expensive candy should she use?

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 4: Systems of Linear Equations

The graphs below represent the supply and demand for a product at various prices per unit. Approximately how many units should be produced so that supply equals demand?

A woman made a deposit of $260\$ 260$260 . If her deposit consisted of 100 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 23 coins with a total face value of $4.55\$ 4.55$4.55 , how many of the coins are nickels?

Tell how many solutions the system has. Do not actually solve. - 2x−y=52 x-y=52x−y=5 −4x+2y=−18-4 x+2 y=-18−4x+2y=−18

What is the graph of an equation in three variables?

x+y+z=7x+y+z=7x+y+z=7 x−y+2z=7x-y+2 z=7x−y+2z=7 5x+y+z=115 \mathrm{x}+\mathrm{y}+\mathrm{z}=115x+y+z=11

Anne and Nancy use a metal alloy that is 19%19 \%19% copper to make jewelry. How many ounces of an alloy that is 12%12 \%12% copper must be mixed with an alloy that is 25%25 \%25% copper to form 65 ounces of the desired alloy?

Without solving the following system of equations, tell what the solution is. Explain your answer. 3x-6y-3z =2 -18x+36y+18z =-12 3x-3y-2z =-5

Solve the problem using a system of equations. -Anne and Nancy use a metal alloy that is 18.4%18.4 \%18.4% copper to make jewelry. How many ounces of a 17%17 \%17% alloy must be mixed with a 19%19 \%19% alloy to form 110 ounces of the desired alloy?

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - x−3y=−3x-3 y=-3x−3y=−3 7x−2y=−217 \mathrm{x}-2 \mathrm{y}=-217x−2y=−21

Decide whether the ordered pair is a solution of the given system - x+y=7x+y=7x+y=7 x−y=3;(−5,2)\mathrm{x}-\mathrm{y}=3 ;(-5,2)x−y=3;(−5,2)

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - y=13−6xy=13-6 xy=13−6x x+6y=−27x+6 y=-27x+6y=−27

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - −7x+9y=−42-7 x+9 y=-42−7x+9y=−42 −5x+2y=−30-5 x+2 y=-30−5x+2y=−30

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - x-y+2z=2 5x+z=0 x+4y+z=-8

The table shown was generated by a graphing calculator. The functions defined by y1y_{1}y1​ and y2 are linear. Based on the table, solve the system of equations formed by y1\mathrm{y}_{1}y1​ and y2\mathrm{y}_{2}y2​ .

The side of an equilateral triangle is 3 inches shorter than the side of a square. The perimeter of the square is 37 inches more than the perimeter of the triangle. Find the length of a side of the square.

A cruise boat travels 36 miles downstream in 3 hours and returns to its starting point upstream in 6 hours. Find the speed of the stream.

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - x−3y=3x-3 y=3x−3y=3 x=8+3yx=8+3 yx=8+3y

Ellen wishes to mix candy worth $2.12\$ 2.12$2.12 per pound with candy worth $3.71\$ 3.71$3.71 per pound to form 26 pounds of a mixture worth $2.73\$ 2.73$2.73 per pound. How many pounds of the more expensive candy should she use?

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

A woman made a deposit of $\$ 260$ . If her deposit consisted of 100 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 23 coins with a total face value of $\$ 4.55$ , how many of the coins are nickels?

Tell how many solutions the system has. Do not actually solve. - $2 x-y=5$ $-4 x+2 y=-18$

$x+y+z=7$ $x-y+2 z=7$ $5 \mathrm{x}+\mathrm{y}+\mathrm{z}=11$

Anne and Nancy use a metal alloy that is $19 \%$ copper to make jewelry. How many ounces of an alloy that is $12 \%$ copper must be mixed with an alloy that is $25 \%$ copper to form 65 ounces of the desired alloy?

Solve the problem using a system of equations. -Anne and Nancy use a metal alloy that is $18.4 \%$ copper to make jewelry. How many ounces of a $17 \%$ alloy must be mixed with a $19 \%$ alloy to form 110 ounces of the desired alloy?

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $x-3 y=-3$ $7 \mathrm{x}-2 \mathrm{y}=-21$

Decide whether the ordered pair is a solution of the given system - $x+y=7$ $\mathrm{x}-\mathrm{y}=3 ;(-5,2)$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $y=13-6 x$ $x+6 y=-27$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $-7 x+9 y=-42$ $-5 x+2 y=-30$

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $x-3 y=3$ $x=8+3 y$

Ellen wishes to mix candy worth $\$ 2.12$ per pound with candy worth $\$ 3.71$ per pound to form 26 pounds of a mixture worth $\$ 2.73$ per pound. How many pounds of the more expensive candy should she use?