Q: After multiplying the first equation by 4 and the second by 5, what are the new equations? $$\begin{cases} 4x - 5y = 17 \\ 3x + 4y = -26 \end{cases}$$

$$\begin{cases} 16x - 20y = 68 \\ 15x + 20y = -130 \end{cases}$$

Question 1

Solve the following system of equations using the addition (elimination) method:

$$\begin{cases} 4x - 5y = 17 \ 3x + 4y = -26 \end{cases}$$

What is the solution $$(x, y)$$?

Accepted Answer

$$(x, y) = (2, -5)$$

Question 2

Which of the following is the first step in using the addition method to solve the system below?

$$\begin{cases} 4x - 5y = 17 \ 3x + 4y = -26 \end{cases}$$

Accepted Answer

Multiply the first equation by 4 and the second by 5 to align the $$y$$ coefficients for elimination.

Question 3

After multiplying the first equation by 4 and the second by 5, what are the new equations?

$$\begin{cases} 4x - 5y = 17 \ 3x + 4y = -26 \end{cases}$$

Accepted Answer

$$\begin{cases} 16x - 20y = 68 \ 15x + 20y = -130 \end{cases}$$

Question 4

What is the result when you add the two new equations from the previous step?

$$\begin{cases} 16x - 20y = 68 \ 15x + 20y = -130 \end{cases}$$

Accepted Answer

$$31x = -62$$

Question 5

What is the value of $$x$$ after solving $$31x = -62$$?

Accepted Answer

$$x = -2$$

Question 6

Substitute $$x = -2$$ into the first equation $$4x - 5y = 17. $$What is the value of $$y$$?

Accepted Answer

$$y = -5$$

Question 7

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

$$\begin{cases} 4x - 5y = 17 \ 3x + 4y = -26 \end{cases}$$

Accepted Answer

$$(-2, -5)$$

Question 8

If you substitute $$x = -2$$ and $$y = -5$$ into the second equation $$3x + 4y = -26$$, what do you get?

Accepted Answer

$$-6 - 20 = -26$$

Question 9

Which of decks below best describes the addition (elimination) method for solving systems of equations?

Accepted Answer

Multiply one or both equations by a number so that when you add or subtract the equations, one variable is eliminated.

Question 10

A chemist is mixing two solutions. The first solution contains $$4x$$ grams of substance A and $$-5y$$ grams of substance B, totaling $$17$$ grams. The second solution contains $$3x$$ grams of substance A and $$4y$$ grams of substance B, totaling $$-26$$ grams. What are the values of $$x$$ and $$y$$?

Accepted Answer

$$x = -2, y = -5$$

Solving Systems of Equations Using the Addition (Elimination) Method

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