Q: Which of the following systems would have no solution?

$$\begin{cases} y = 4x + 1 \\ 2y - 8x = 10 \end{cases}$$

Question 1

Given the system of equations:

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

What is the solution $$(x, y) to $$the system using the substitution method?

Accepted Answer

$$(x, y) = (2, 9)$$

Question 2

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

Accepted Answer

$$8x + 2 - 4x = 14$$

Question 3

What is the value of $$x$$ after solving the equation $$8x + 2 - 4x = 14$$?

Accepted Answer

$$x = 2$$

Question 4

Once you have found $$x = 2$$, what is the value of $$y$$ using the equation $$y = 4x + 1$$?

Accepted Answer

$$y = 9$$

Question 5

Which of the following best describes the substitution method for solving systems of equations?

Accepted Answer

Solving one equation for one variable and substituting that expression into the other equation.

Question 6

If you substitute $$x = 2$$ and $$y = 9$$ into the second equation $$2y - 4x = 14$$, what do you get?

Accepted Answer

$$2(9) - 4(2) = 18 - 8 = 14 ($$which satisfies the equation)

Question 7

Which of the following is the first step in the substitution method for the given system?
$$\begin{cases} y = 4x + 1 \ 2y - 4x = 14 \end{cases}$$

Accepted Answer

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

Question 8

If the system of equations had been $$y = 4x + 1$$ and $$2y + 4x = 14$$, what would be the value of $$x$$ after substitution?

Accepted Answer

$$x = 1$$

Question 9

Which of the following systems would have no solution?

Accepted Answer

$$\begin{cases} y = 4x + 1 \ 2y - 8x = 10 \end{cases}$$

Question 10

Which real-world scenario could be modeled by the system $$\begin{cases} y = 4x + 1 \ 2y - 4x = 14 \end{cases}$$?

Accepted Answer

A company charges a base fee of $$1 and 4 $$per hour for a service, and a customer is charged twice the total cost minus four times the hours for a total of $14.

Solving Systems of Equations Using Substitution

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