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

Answers

Answer 1

Answer:
Let's write both equations in the standard form of [ y = mx + b ],
and then see what we can tell about their graphs.

First equation:   x + 3y = 9
Subtract 'x' from each side: 3y = -x + 9
Divide each side by 3: y = -1/3 x + 3
This line crosses the y-axis at y=3, and it has a slope of -1/3 .

Second equation:    3x - y = 7
Subtract 3x from each side: -y = -3x + 7
Multiply each side by -1 : y = 3x - 7
This line crosses the y-axis at y=-7, and it has a slope of 3 .

-- The two lines have different slopes, so they're not parallel.
They must intersect somewhere.
-- They're not the same line, so they can't 'intersect' everywhere.
-- They have slopes of -1/3 and 3 . Their slopes are negative reciprocals,
so the lines are perpendicular.

All of this says that the two equations can't have no solution, and they can't have
infinitely many solutions. They must have one and only one solution.
I guess that means that it's our job to find it now.

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

For each equation, the "mx + b" form is equal to 'y' . Since these two things are
equal to the same thing, they must be equal to each other, and we can write:

   -1/3 x + 3 = 3x - 7

Multiply each side by 3 : -x + 9 = 9x - 21

Add 'x' to each side: 9 = 10x - 21

Add 21 to each side:    30 = 10x

Divide each side by 10 : 3 = x

The intersection/solution is some place where x=3 .
Let's put that back into the first equation:

   x + 3y = 9

   3 + 3y = 9

Subtract 3 from each side:   3y = 6

Divide each side by 3 : y = 2

And there's your solution: x = 3
   y = 2
On the graph, the two lines intersect at the point (3, 2) .

We used the first equation to get part of the solution, so we can't use
the same equation to check the solution. We'll put our solution into the
second equation, and see whether it checks there:

   3x - y = 7

3(3) - (2) = 7

   9 - 2 = 7

   7 = 7 yay !

The two equations have one and only one solution,
and it is definitely x = 3, y = 2 .

Answer 2

Answer:

Substitution or Elimination

im using substitution

1. solve for variable for one of the equation

x + 3y = 9

x = 9 - 3y

2. Substitute the variable into one of the equation

3 (9-3y) - y = 7

27 - 9y - y = 7

27 - 10y = 7

-10y = 7 - 27

-10y = -20

y = 2

3. sub y = 2 into any equation to find x

3x - 2 = 7

3x = 7 -2

3x = 5

x = 5/3

X+3(2) = 9

x + 6 = 9

x = 9-6

x= 3

therefore there are two solutions x = 3 and x= 5/3

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Answers

Answer:

Its F(x)=-1/4x-1/4

Step-by-step explanation:

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Answers

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Find the difference 9/11-5/12

Answers

First we need to find a common denominator. For this one, the easiest way to do that is multiply 11 x 12 = 132

now convert the numerator

9x12 = 108
5x11 = 55

108/132 - 55/132 =

now just subtract the numerators

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A blouse require 1 ¼ m of cloth, how many blouses can be made from 21 m of clothA. 12
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Answers

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Round .0091 to the thousandths

Answers

The answer is 0.009.
Hope this helps!:)

0.0091 rounded to the nearest thousandths would be 0.009. This is because the 1 after the 9 is BEFORE 5 so it stays as 9, and we remove the 1.

Answer:- .0091 rounded to the nearest thousandths is .009.

Hope I helped ya!! xD

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