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Greeley [361]
3 years ago
14

Step by step linear combination. 3x+2y=-4 4x-y=13

Mathematics
1 answer:
Paraphin [41]3 years ago
5 0

Answer:

The solution is the point (2,-5)

Step-by-step explanation:

we have

3x+2y=-4 ------> equation A

4x-y=13 ------> equation B

Multiply equation B by 2 both sides

2(4x-y)=2*13

8x-2y=26 ------> equation C

Adds equation A and equation C

3x+2y=-4\\8x-2y=26\\---------\\3x+8x=-4+26\\11x=22\\x=2

Find the value of y

substitute the value of x in equation A

3(2)+2y=-4

2y=-4-6

2y=-10  

y=-5  

The solution is the point (2,-5)

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A bacteria culture starts with 100 bacteria and doubles in size every half hour.
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y=25600

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If j and k are nonzero integers, which pair of points must lie in the same quadrant?
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<h3>Answer:  Choice D.   (3j, 3k)  and (3/j, 3/k)</h3>

The slash indicates a fraction.

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

Proof:

We'll need to consider 4 different cases.

-----------------------

Case (1): j > 0 and k > 0

If j > 0, then 3j > 0 and 3/j > 0

If k > 0, then 3k > 0 and 3/k > 0

The two points (3j, 3k) and (3/j, 3/k) are both in quadrant 1.

-----------------------

Case (2): j > 0 and k < 0

If j > 0, then 3j > 0 and 3/j > 0

If k < 0, then 3k < 0 and 3/k < 0

Points (3j, 3k) and (3/j, 3/k) are both in quadrant 4.

------------------------

Case (3): j < 0 and k > 0

If j < 0, then 3j < 0 and 3/j < 0

If k > 0, then 3k > 0 and 3/k > 0

Points (3j, 3k) and (3/j, 3/k) are in quadrant 3.

------------------------

Case (4): j < 0 and k < 0

If j < 0, then 3j < 0 and 3/j < 0

If k < 0, then 3k < 0 and 3/k < 0

Points (3j, 3k) and (3/j, 3/k) are in quadrant 4.

------------------------

For nonzero integers j and k, we've shown that Points (3j, 3k) and (3/j, 3/k) are in the same quadrant. This concludes the proof.

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