Question 1

Solve the following system of equations using the substitution method:

$$
\begin{cases}
y = 4x + 1 \
2y - 4x = 14
\end{cases}
$$

What is the solution to the system?

Accepted Answer

The solution is $$(3, 13).$$

Question 2

Which of the following best describes the first step in solving the system below by substitution?

$$
\begin{cases}
y = 4x + 1 \
2y - 4x = 14
\end{cases}
$$

Accepted Answer

Substitute $$y = 4x + 1$$ into $$2y - 4x = 14.$$

Question 3

After substituting $$y = 4x + 1$$ into $$2y - 4x = 14$$, what equation do you get?

Accepted Answer

$$2(4x + 1) - 4x = 14$$

Question 4

Solve for $$x in $$the equation $$2(4x + 1) - 4x = 14.$$

Accepted Answer

$$x = 3$$

Question 5

Once you have found $$x = 3$$, what is the value of $$y in $$the system?

$$
y = 4x + 1$$

Accepted Answer

$$y = 13$$

Question 6

Which of the following ordered pairs is the solution to the system?

$$
\begin{cases}
y = 4x + 1 \
2y - 4x = 14
\end{cases}
$$

Accepted Answer

$$(3, 13)$$

Question 7

If you graph the equations $$y = 4x + 1$$ and $$2y - 4x = 14$$, what do you expect to see?

Accepted Answer

The lines intersect at one point.

Question 8

Which of the following statements is true about the solution to the system?

$$
\begin{cases}
y = 4x + 1 \
2y - 4x = 14
\end{cases}
$$

Accepted Answer

There is exactly one solution.

Question 9

Which of the following is a correct interpretation of the solution $$(3, 13) in a $$real-world context?

Accepted Answer

When $$x = 3$$, $$y = 13$$ satisfies both equations simultaneously.

Question 10

Suppose the system represented the cost $$y of $$buying $$x$$ items with a fixed fee. If $$y = 4x + 1$$ and $$2y - 4x = 14$$, what is the cost for 3 items?

Accepted Answer

$$13$$

Solving a System of Equations Using Substitution

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