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joja [24]
3 years ago
13

Which statements about the system are true?

Mathematics
1 answer:
Kruka [31]3 years ago
5 0

2 Answers:

  • B)  The lines are parallel
  • C)  The lines have the same slope.

Parallel lines always have equal slope, but different y intercepts.

==========================================================

Explanation:

Let's solve the second equation for y

3y - x = -7

3y = -7+x

3y = x-7

y = (x-7)/3

y = x/3 - 7/3

y = (1/3)x - 7/3

The equation is in y = mx+b form with m = 1/3 as the slope and b = -7/3 as the y intercept. We see that the first equation, where y was already isolated, also has a slope of m = 1/3. The two equations of this system have the same slope. Choice C is one of the answers.

However, they don't have the same y intercept. The first equation has y intercept b = -4, while the second has b = -7/3. This means that they do not represent the same line. They need to have identical slopes, and identical y intercepts (though the slope can be different from the y intercept of course) in order to have identical lines. So we can rule out choice D and E because of this.

Because the two equations have the same slope, but different y intercepts, this means the lines are parallel. Choice B is the other answer.

Parallel lines never touch or intersect, which in turn means there is no solution point. A solution point is where the lines cross. We can rule out choice A.

I recommend using your graphing calculator, Desmos, GeoGebra, or any graphing tool (on your computer or online) to graph each equation given. You should see two parallel lines forming. I used GeoGebra to make the graph shown below.

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Answer:

9/20 yes, 4/15 not. See below

Step-by-step explanation:

Pick 9/20 and multiply numerator and denominator by 5:

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We know that if we divide a number by 100 we need to move the coma as two places left, so:

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On the other hand if we pick 4/15 let try to divide it (here I will do it 'manually'):

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we can divide 4 by 15, so we use 40 and begin with a comma

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So, we will have 0.266666666666666 infinitely. The decimal for 4/15 is non terminating and is 0.26666666666666666...

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3 years ago
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