Question 1

Which of the following is the first step in solving a system of linear equations by the substitution method?

Accepted Answer

Solve either equation for one variable in terms of the other.

Question 2

Given the system: 
$$\begin{cases} y = 2x - 1 \ 3x + y = 8 \end{cases}$$
What is the solution to the system?

Accepted Answer

$$(3, 5)$$

Question 3

If you solve a system of equations by substitution and end up with the statement $$0 = 5$$, what does this indicate about the system?

Accepted Answer

The system is inconsistent and has no solution.

Question 4

Solve the following system using substitution:
$$\begin{cases} x + y = 4 \ x - y = 2 \end{cases}$$

Accepted Answer

$$(3, 1)$$

Question 5

Which of the following statements is true about a system of equations that results in a true statement such as $$6 = 6$$ after substitution?

Accepted Answer

The system has infinitely many solutions.

Question 6

Given the system:
$$\begin{cases} y = 4x + 2 \ 2y - 8x = 4 \end{cases}$$
What is the solution?

Accepted Answer

Infinitely many solutions

Question 7

A supply and demand model is given by:
$$\begin{cases} p = 50 - 2x \ p = 10 + 3x \end{cases}$$
where $$p is $$price and $$x is $$quantity in thousands. What is the equilibrium price?

Accepted Answer

$$30$$

Question 8

If a system of equations is dependent, which of the following is true?

Accepted Answer

The system has infinitely many solutions.

Question 9

Solve the following system by substitution:
$$\begin{cases} y = 2x + 1 \ 4x - 2y = -2 \end{cases}$$

Accepted Answer

$$(0, 1)$$

Question 10

A company finds that the demand for its product is given by $$p = 100 - 5x$$ and the supply is $$p = 20 + 3x$$, where $$p is $$the price and $$x is $$the quantity in hundreds. What is the equilibrium quantity?

Accepted Answer

$$10$$

Question 11

Which of the following best describes the solution set of the system:
$$\begin{cases} y = 2x + 3 \ 4x - 2y = -6 \end{cases}$$

Accepted Answer

Infinitely many solutions

Question 12

If you substitute one equation into another and end up with $$0 = 0$$, what does this mean about the system?

Accepted Answer

The system has infinitely many solutions.

Question 13

Solve the system by substitution:
$$\begin{cases} x = 2y + 1 \ 3x - 6y = 3 \end{cases}$$

Accepted Answer

$$(3, 1)$$

Question 14

Which of the following is a necessary step when checking your solution to a system of equations solved by substitution?

Accepted Answer

Substitute the values into both original equations to verify they are true.

Question 15

A system of equations models the intersection of two lines. If the lines are parallel, what can you conclude about the system?

Accepted Answer

The system is inconsistent and has no solution.

Solving Systems of Linear Equations by the Substitution Method

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