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Couldn’t figure this out help please

Couldn’t figure this out help please-example-1
User Treborbob
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2 Answers

17 votes
17 votes

(B)

Explanation:

Rewrite the equations into their standard forms. The first one can be rewritten as


10x - 12y = -5

and the 2nd can be rewritten as


3x + 5y = -1

Solving this system either by substitution or elimination, we get


x = -(37)/(86)\:\:\text{and}\:\:y= (25)/(86)

If you add x + y, you'll get a negative number.

User FaultyBagnose
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2.3k points
19 votes
19 votes

9514 1404 393

Answer:

B. x + y < 0

Explanation:

The two equations can be cleared of fractions by multiplying by 15.

15(2/3(x +1) -4/5y) = 15(1/3)

10(x +1) -12y = 5

10x -12y = -5

and

15(2/5x +1/3(2y +1)) = 15(1/5)

6x +5(2y +1) = 3

6x +10y = -2

3x +5y = -1 . . . . . eliminate common factor of 2

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You can find the solutions any way you like, but you can answer the question without doing that. The lines are not parallel, nor coincident, so there is exactly one solution. (choices C and D are incorrect)

If we can locate the solution relative to the line x + y = 0, we can tell if choice A or choice B is correct. A quick look at the intercepts of the equations tells us the solution cannot lie in quadrants 1 or 4. The negative y-intercept and shallow slope (-3/5) of the second equation tells us the solution must lie below the line x + y = 0. That means x+y < 0, choice B.

_____

In the attached graph, the line x+y=0 is dashed orange. Above that line, x+y>0; below that line, x+y<0. We see the intersection point of the red and blue lines is in the region where x+y < 0.

For standard form equation ax+by = c, the x- and y-intercepts are c/a and c/b, respectively, so are easy to find from that form. Knowing these makes it easy to make a sketch of the graph, locating the solution point relative to the line x+y = 0.

Couldn’t figure this out help please-example-1
User Julien BONNIN
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2.9k points