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Many questions -- Substitute method, slope, graph lines.

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1. Determine the x- and y-intercepts of the given equation. Show your work. Then plot the intercepts, and graph the line.
-5x + y = 0

2. Determine the x- and y-intercepts (if any) of the given equation. Show your work. Then plot the intercepts, and graph the line
7x + 56y = 0

3. Select the line that has the given slope and y-intercept.

Slope -3; y-intercept (0, -6)

4. Find the slope and the y-intercept of the line.
y - 7 = 8

5. Find an equation in point-slope form of the line having the specified slope and containing the point indicated.

m = -8; (6, 9)

6. Find an equation of the line meeting the specified conditions. Write your final answer in slope-intercept form.

Containing the point (0, 6) and parallel to y = 4x - 6Graph the line
y - 5 = (x + 4)

7. Solve the problem.

In 1995 the United States recovered 23% of its municipal solid wastes through recycling, up from 17% in 1990. Find an equation for the line whose graph depicts this data (where x is measured in years after 1990).
Find an equation of the line containing the given pair of points. Write your final answer in slope-intercept form.

(3, -5) and (0, -9)
8. Write the equation of the line on the graph in slope-intercept form.

9. Solve using either elimination or substitution. Show your work. If the system has either no solution or an infinite number of solutions, state this.

7x - 2y = 24
5x + 4y = 28
10. Determine wheither each pair of equations represents parallel lines.
Y = -5/2x +1,
Y = 5/4x + 3
11. Graph each equation. Y = 3/2x +1
15 Solve using the substitute method.
5x + 6y = 14,
-3y + x = 7

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Discussion questions on systems of linear equations

Please provide an answer to the following questions below that contains 250 to 300 words each.

1.By looking at two linear equations, how can you tell that the corresponding lines are parallel, the same graph, or intersecting lines? How many solutions does each possibility have and why is that? Show examples for each possible situation.

2.Is there a difference between solving a system of equations by the algebraic method and the graphical method? Why? What are the advantages and disadvantages of each?

3.Write 250-300 words comparing and contrasting all methods of solving systems of linear equations with two variables. Explain which method you prefer and why. Support your answer by appropriate examples.

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