Deck 1: Linear Equations

Question 1

Use back-substitution to solve the system of linear equations.

A)
B)
C)
D)
E)

Answer 1

Question 2

Solve the system of equations by using graphical methods.

A)
B)
C)
D)
E) There are infinitely many solutions.

Answer 2

There are infinitely many solutions.

Question 3

Solve the system of equations by using graphical methods.

A)
B)
C)
D)
E) There is no solution to the equations.

Answer 3

Question 4

Solve using any method.

A)
B)
C)
D) , where a is any real number
E) inconsistent

Question 5

Solve the system.

A)
B)
C)
D)
E)

Question 6

Solve the system of linear equations.

A)
B)
C)
D)
E)

Question 7

Solve the system of linear equations.

A)
B)
C)
D)
E)

Question 8

Solve the system of linear equations.

A)
B)
C)
D)
E)

Question 9

Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.

A) row-echelon form
B) row-echelon form and reduced row-echelon form
C) neither

Question 10

Find the solution set of the system of linear equations in the variables x and y (in that order) that has the following augmented matrix.

A)
B)
C)
D)
E)

Question 11

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables x, y, and z.)

A)
B)
C)
D)
E)

Question 12

The given matrix is an augmented matrix representing a system of linear equations. Find the solution of the system.

A)
B)
C)
D)
E)

Question 13

Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

A)
B)
C)
D)
E) no solution

Question 14

Use Gaussian elimination method to solve the system of linear equations.

A)
B)
C)
D)
E) inconsistent system

Question 15

Solve the following system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. If there is no solution, state that the system is inconsistent.

A)
B)
C)
D) inconsistent system
E)

Question 16

Find the equation of the parabola that passes through the points .

A)
B)
C)
D)
E)

Question 17

Find the equation of the circle that passes through the points .

A)
B)
C)
D)
E)

Question 18

Suppose that the U. S. population for the years 1920, 1930, 1940, and 1950 is shown in the table below. Let x represent the number of decades since 1920. Find a cubic polynomial that fits these data

A)
B)
C)
D)
E)

Question 19

Suppose that the U. S. population for the years 1920, 1930, 1940, and 1950 is shown in the table below. Let x represent the number of decades since 1920. Estimate the population in 1970 by using a cubic polynomial that fits these data.

A) 448 million
B) 278 million
C) 236 million
D) 298 million
E) 210 million

Question 20

Suppose that the net profit (in millions of dollars) for Microsoft from 2000 to 2007 is shown in the table below.
A cubic model that matches the data for the years 2001, 2003, 2005, and 2007 is to be determined where x represents the number of years since 2000. Set up a system of equations to solve for the coefficients a₀, a₁, a₂ and a₃.

A)
B)
C)
D)
E)

Question 21

Irrigation. An irrigation system allows water to flow in the pattern shown in the figure below. Water flows into the system at A and exits at B, C, D, and E with the amounts shown. Using the fact that at each point the water entering equals the water leaving, formulate an equation for water flow at each of the five points and solve the system.

A) , , , , (in thousands of gallons)
B) , , , , (in thousands of gallons)
C) , , , , (in thousands of gallons)
D) , , , , (in thousands of gallons)
E) , , , , (in thousands of gallons)

Question 22

Traffic flow. In the analysis of traffic flow, a certain city estimates the following situation for the "square" of its downtown district. In the following figure, the arrows indicate the flow of traffic. If x₁ represents the number of cars traveling between intersections A and B, x₂ represents the number of cars traveling between B and C, x₃ the number between C and D, and x₄ the number between D and A, we can formulate equations based on the principle that the number of vehicles entering an intersection equals the number leaving it. That is, for intersection A we obtain

Formulate equations for the traffic at B, C, and D. Solve the system of these four equations.

A) , , ,
B) , , ,
C) , , ,
D) , , ,
E) , , ,

Question 23

Applying Kirchhoff's Laws to the electrical network in the figure, the currents I₁, I₂, and I₃ are the solution of the system

A) amperes; amperes; amperes
B) amperes; amperes; amperes
C) amperes; amperes; amperes
D) amperes; amperes; amperes
E) amperes; amperes; amperes

Question 24

Write the partial fraction decomposition of the rational expression.

A)
B)
C)
D)
E)

Question 25

Use a system of equations to write the partial fraction decomposition of the rational expression .
Then solve the system using matrices.

A)
B)
C)
D)
E)