Question 1

Which of the following best describes the solution to a system of two linear equations in two variables?

Accepted Answer

The point where the two lines intersect.

Question 2

Given the system of equations:
$$
\begin{cases}
2x - 3y = -17 \
x - y = -7
\end{cases}

Is $$the point $$(1, -6) a $$solution to the system?

Accepted Answer

No, because it does not satisfy either equation.

Question 3

How many solutions does a system of two linear equations in two variables have if the lines are coincident?

Accepted Answer

Infinitely many solutions.

Question 4

Which method is generally NOT recommended for solving systems of linear equations in two variables?

Accepted Answer

Graphing.

Question 5

Solve the system by substitution:
$$
\begin{cases}
x + 6y = 5 \
x - 3y = -4
\end{cases}
$$
What is the value of $$y$$?

Accepted Answer

$$y = -1$$

Question 6

Which of the following is the correct first step when using the elimination (addition) method to solve a system of equations?

Accepted Answer

Write both equations in standard form $$Ax + By = C.$$

Question 7

Solve the system by elimination:
$$
\begin{cases}
4x + 6y = 13 \
5x + 6y = -1
\end{cases}
$$
What is the value of $$x$$?

Accepted Answer

$$x = -14$$

Question 8

Brandon and Archer are working out at the gym. Brandon does 3 reps and Archer does 5 reps. The combined total amount lifted is 2170 pounds. If each rep lifts the same amount, how much does each rep weigh?

Accepted Answer

$$271$$ pounds

Question 9

Given the system:
$$
\begin{cases}
3x + 2y = 4 \
5y + 4x = -7
\end{cases}
$$
Which method would be most efficient to solve this system?

Accepted Answer

Elimination (Addition)

Question 10

If a system of equations has no solution, what can be said about the graphs of the equations?

Accepted Answer

The lines are parallel.

Question 11

Solve the system by elimination:
$$
\begin{cases}
5x + 6y = -3 \
20x - 24y = 12
\end{cases}
$$
What is the value of $$y$$?

Accepted Answer

$$y = -2$$

Question 12

Which of the following is NOT a possible outcome when solving a system of two linear equations in two variables?

Accepted Answer

Exactly two solutions.

Question 13

A system of equations is called dependent if:

Accepted Answer

The equations have infinitely many solutions.

Question 14

Which of the following is the correct standard form for a linear equation in two variables?

Accepted Answer

$$Ax + By = C$$

Question 15

If you solve a system of equations and get a false statement such as $$0 = 5$$, what does this indicate?

Accepted Answer

The system has no solution.

Question 16

Which step is necessary before adding two equations together in the elimination method?

Accepted Answer

Multiply one or both equations by constants to create opposite coefficients for one variable.

Question 17

Given the system:
$$
\begin{cases}
2x + 6y = 10 \
4x + 12y = 20
\end{cases}
$$
What type of solution does this system have?

Accepted Answer

Infinitely many solutions.

Question 18

Which of the following real-world scenarios can be modeled by a system of linear equations?

Accepted Answer

Calculating the intersection point of two roads.

Question 19

Solve the system by substitution:
$$
\begin{cases}
2x + 4y = 5 \
x - 3y = -4
\end{cases}
$$
What is the value of $$x$$?

Accepted Answer

$$x = 8$$

Question 20

When using the substitution method, what is the first step?

Accepted Answer

Solve one of the equations for one variable in terms of the other.

Systems of Linear Equations in Two Variables: Methods and Applications

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