Free Practice Quiz Question List

12/14 12. Systems of Equations and Inequalities Online Quiz Questions

Use this free practice quiz with 20 questions to review 12/14 12. Systems of Equations and Inequalities, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

A system of two linear equations has two distinct parallel lines as its graphs. How many solutions does the system have?

A
One solution
B
No solutions
C
Infinitely many solutions
D
Three solutions

Choose one

1 point

Use elimination to solve the system: $2x+y=11$ and $4x-y=7$ . Which ordered pair is the solution?

A
(2, 7)
B
(4, 3)
C
(3, 5)
D
(5, 1)

Choose one

1 point

When graphing the inequality $y\geq 3x-4$ , how should the boundary line be drawn?

A
A solid boundary line
B
A dashed boundary line
C
No boundary line
D
A vertical boundary line regardless of the equation

Choose all

1 point

Which operations are valid elementary row operations that preserve a system's solution set? Select all that apply.

A
Interchange two rows.
B
Multiply a row by a nonzero constant.
C
Add a multiple of one row to another row.
D
Multiply a row by zero.
E
Delete a row without checking its equation.

Choose all

1 point

A workshop makes tables $t$ and chairs $c$ . Each table uses 4 cutting hours and 2 assembly hours; each chair uses 1 cutting hour and 2 assembly hours. The workshop has at most 40 cutting hours and 24 assembly hours. Which constraints correctly model the available hours? Select all that apply.

A
$4t+c\leq 40$
B
$2t+2c\leq 24$
C
$4t+c=40$ must hold for every feasible plan.
D
$t+c\geq 40$

True or false

1 point

True or false: If solving a system by substitution produces the statement $0=5$ , then the system has no solution.

A
True
B
False

True or false

1 point

True or false: If the coefficient matrix of a two-variable system has determinant zero, the system does not have a unique solution.

A
True
B
False

Written response

1 point

For the system $y=2x+1$ and $3x+y=16$ , what is the value of $x$ ?

Written response

1 point

A company's cost is $C(x)=12x+3000$ and its revenue is $R(x)=20x$ . How many units must be produced and sold to break even?

Fill in the blank

1 point

For a system written as $A\mathbf{x}=\mathbf{b}$ , $A$ is the and $\mathbf{b}$ is the .

Fill in the blank

1 point

Use a line for an inequality with $\leq$ or $\geq$ , and a line for an inequality with $<$ or $>$ .

Open ended

1 point

How many liters of a 20% solution and a 50% solution are needed to make 10 liters of a 32% solution? Set up a system, solve it, and explain what each solution value means.

Choose one

1 point

Solve the three-variable system: $x+y+z=6$ , $2x-y+z=3$ , and $x+2y-z=2$ . Which ordered triple is the solution?

A
$(2,1,3)$
B
$(1,3,2)$
C
$(3,2,1)$
D
$(1,2,3)$

Choose one

1 point

The graphs of $y=2x+1$ and $y=-x+7$ intersect at which point?

A
$(2,4)$
B
$(2,5)$
C
$(3,5)$
D
$(5,2)$

Choose one

1 point

A workshop uses the constraints $4t+c\le40$ , $2t+2c\le24$ , $t\ge0$ , and $c\ge0$ . Is the production plan $(t,c)=(6,8)$ feasible?

A
Yes, because both quantities are nonnegative.
B
Yes, because the cutting-hours constraint is satisfied.
C
No, because the assembly-hours constraint is exceeded.
D
No, because the number of tables is greater than the number of chairs.

Choose one

1 point

How many solutions does the system $y=2x-3$ and $2x-y=3$ have?

A
Exactly one solution
B
No solution
C
Infinitely many solutions
D
Exactly two solutions

Choose one

1 point

When graphing the system $y\ge3x-1$ and $y<-x+5$ , which boundary-line styles are correct?

A
Draw $y=3x-1$ solid and $y=-x+5$ dashed.
B
Draw $y=3x-1$ dashed and $y=-x+5$ solid.
C
Draw both boundary lines solid.
D
Draw both boundary lines dashed.

True or false

1 point

True or false: Each of the three elementary row operations preserves the solution set of a system of linear equations.

A
True
B
False

Written response

1 point

A company has cost $C(x)=12x+3000$ and revenue $R(x)=20x$ . What is the break-even production level, in units?

Written response

1 point

How many liters of the 50% solution are needed to make 10 liters of a 32% solution from 20% and 50% solutions?