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2. Given the system, answer the following questions:

y= 6+ 2x
8x - 4y = -20
Which method would you use to solve this system (Equal Values, Substitution, Elimination, Graphing)? Why?
a.
b. Solve the system using this method. Show your work below.
C. Explain what your answer tells us about the two lines of the system of equations if they were graphed?

1 Answer

4 votes

Answer:

Explanation:

y= 6+ 2x

8x - 4y = -20

a. My personal choice for how to solve this system of equations depends on how complex the equations are. Anything that is nonlinear, e.g., x^2 for example, I'll using graphing. For this particular system, I would go with either substitution or, if my computer is handy, go to the free DESMOS graphing site and find the intersection of the plotted lines. I don't know what "equal values" is, so I can't comment. Substitution and elimination are really the same thing, in my view.

I'll solve using both substitution and graphing:

Substitution:

y= 6+ 2x

8x - 4y = -20

We can use the first equation definition of y (6+2x) in the second equation:

8x - 4y = -20
8x - 4(6+2x) = -20

8x - 24 - 8x = -20

0x = 4

Well, that didn't work out well . . . .

Maybe I did something wrong. Let's try:

Graphing:

See the attached graph.

Zounds (metric term for "that's odd")

The lines appear parallel. If so, there is no solution - they never intersect. [They have a lot in common, too bad they'll never meet.]

Let's rewrite both equations in slope/intercept format of y = mx + b, where m is the slope and b is the y intercept (the value of y when x = 0)

---

y= 6+ 2x

y = 2x + 6

This line has a slope of 2, with an intercept of 6

8x - 4y = -20

-4y = -8x - 20

y = 2x + 5

This line also has a slope of 2, with an intercept of 5,

The lines are parallel so there is no solution. I should have rewritten both in slope-intercept form as a first step. One would spot the same slope and finished the problem: no solution. Using the DESMOS graphing tool was just as easy, and it helps build confidence in what is happening.

2. Given the system, answer the following questions: y= 6+ 2x 8x - 4y = -20 Which-example-1
User Kmek
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