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3 years ago

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find

all solutions whenever they exist.
X + 3y = 9

3x –y = 7

Mathematics

1 answer:

Blababa [14]3 years ago

4 0

$After\ adding\ equations\ and\ simplifying:\\\\One\ solution:\\\\x=number\\ example: x=2\\\\ infinitely\ many\ solutions:\\\\ Left\ side=\ Right\ side\\ example:\\ 2=2\\\\ No\ solutions:\\\\2 \neq 5$ $\left \{ {{x+3y=9} \atop {3x-y=7}\ \ |*3} \right.\\\\ \left \{ {{x+3y=9} \atop {9x-3y=21}} \right.\\+--------\\\\Addition\ method:\\\\10x=30\ \ |:10 \\\\x=3\\\\x+3y=9\\\\3y =9-x=9-3=6\\\\y=2\\\\ \left \{ {{y=2} \atop {x=3}} \right.$

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The weight of a radioactive isotope was 96 grams at the start of an experiment. After one hour, the weight of the isotope was ha

zimovet [89]

The starting weight of the radioactive isotope = 96 grams

Weight after one hour is half of the starting weight. So the weight of the radioactive isotope after 1 hour = 48 grams

After 2 hours the weight is half as compared to the weight after previous hour. So weight after 2 hours = 24 grams.

This means, after every hour the weight is being halved. The half life of radioactive isotope is one hour.

Since after every hour, the weight is being halved, the weight of the isotope can be modeled by an exponential equation.

So,

Initial Weight = W₁ = 96
Change factor = 1/2 = 0.5

The general equation of the sequence will be:

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3 0

2 years ago

Read 2 more answers

Given the system

Irina-Kira [14]

we have

y > -2 x + y < 4

using a graph tool

see the attached figure

The shaded area is the solution of the system

Part 1) Name an ordered pair that is a solution to this system and explain how you know that this is a solution point

Let

A ( -40,20)

The point A is solution of the system because the point lie on the shaded area

Check

If the point A is solution of the system must satisfy both system inequalities

point A

x=-40

y=20

substitute

y > -2-------> 20 > -2-------> is ok

x + y < 4----> -40+20 < 4-----> -20 < 4-----> is ok

therefore

the answer Part 1) is

The point A is a solution of the system

Part 2) Name an ordered pair that is not a solution to the system and explain how you know that it is not a solution

Let

B(20,20)

The point B is not solution of the system because the point not lie on the shaded area

Check

If the point B is not solution of the system must not satisfy both system inequalities

point B

x=20

y=20

substitute

y > -2 -------> 20 > -2-------> is ok

x + y < 4---->20+20 < 4-----> 40 < 4------> is not ok

therefore

the answer part 2) is

The point B is not a solution to the system

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2 years ago

Write 12/root2 + root18 in the form broot2 where b is an interger

katrin2010 [14]

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