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........eq.1
........eq.2
______________________
........eq.1.......substitute from eq.2
.....solve for

........both sides multiply by






now find
........eq.2




see it on a graph:

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to find the equation of the line that contains the point (,) and has the as the line , first find
....solve for
.......this is form ;so, slope is
now find the equation of the line that contains the point (,) and has the slope

Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out: it goes through point (3, -6) it has a slope of 4 First, let's draw a diagram of the coordinate system with point (3, -6) plotted with a little blue dot: Write this down: the formula for the equation, given point and intercept a, is (see a paragraph below explaining why this formula is correct) Given that a=4, and , we have the equation of the line: Explanation: Why did we use formula ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ): Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: . Here's the graph:

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Let for person to do the job
Let the completed
A shared work equation:
.......reduce the fraction
.....multiply both sides by



....time needed for person to do the job
alone

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.......this is a complex solution, there is no real solution for

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......

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given:
=(,), slope
The slope of a line is because anything divided by zero is undefined.
All you need to do is plot the point and draw a line parallel to y-axis through

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given:
...=>....

then

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an exponential function of the form whose graph passes through the given points (,),(,) you can find if you find first what and is equal to
plug in given points in and find
.......if (,), then



now find

.......if (,), and , then






....round it

so, your exponential function is:

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if one chair cost $
then for chairs you need to pay $

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if the circumferance of the circle is

what is the length of if it is degrees?
since degrees is of full central angle in the circle, the length of the arc will be of the circumferance of the circle is
so,

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to cover the floor of a room whose dimensions are by if the size of each tile is by you first calculate the area of a room and the area of a tile
let the area of a room be and the area of a tile


and

to get number of tiles you need to divide by
since the units are different, first you will need to convert to or to
let's convert to
, so the size of each tile is by which is by
then


now we can divide by



...you will need tiles

or covert to :
by :

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The area of a circle is the number of square units inside that circle.
To calculate it, you use formula: where is a radius and we use a constant

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Suppose we have two functions of a variable ,
1st is and 2nd ,(we can name it
then
....(same as were useing use it as first function and as second
so, we have to find

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If the domain is { , , } (means all values ), you will find the range of if you substitute values in given function:

if ...=>......=>...
if ...=>......=>......=>...
if ...=>......=>......=>...
so, the range is: { , , }

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For sequences, the common difference is , and the first term is often referred to simply as "". Since you get the next term by adding the common difference, the value of is just . The third term is . The fourth term is . Following this pattern, the term an will have the form
.
For sequences, the common ratio is , and the first term is often referred to simply as "". Since you get the next term by multiplying by the common ratio, the value of is just . The third term is . The fourth term is . Following this pattern, the term an will have the form
.
in your case ,,, sequence is have the form
common difference is and the greatest common divisor is
first term is and if divided by , we get that could be written as starting with and up

so, the recursive formula is:

and this is sequence

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..factor




if ...=>...
if ...=>...

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...use quadratic formula












solutions:





and

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take a look at ordered pairs
if then
if then which is actually
if then which is actually
if then which is actually

if then which is actually
so, the relationship between and is:

see it on a graph:

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..first use negative exponent property



...use a power of a power property



....use a quotient property



.....use negative exponent property

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first write in form where is slope and is
...solve for



so, the slope of the line with the equation is

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If , the value of , the you have

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............since , we have

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.....if , then
in that case we will have
so, your answer is:

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....do first
..now multiply by

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given:



Row operation
1:

....multiply the 1st row by 1/3
=>
Row operation
2:
.........add -4 times the 1st row to the 2nd row...=>

Row operation
3:
..............add -6 times the 1st row to the 3rd row=>...
Row operation
4:
....multiply the 2nd row by 3/10..=>...
Row operation
5:
...........multiply the 3rd row by 1/7...=>...
Row operation
6:
.....add -11/10 times the 3rd row to the 2nd row...>...

Row operation
7:
....add -1/3 times the 3rd row to the 1st row...=>...
Row operation
8:
matrix( 1, -1 / 3, -2 / 3, 0,
0 , 1 , 11 / 10, 0,
0, 0, 0, 1
)
)}}}.......add 1/3 times the 2nd row to the 1st row....=>
matrix( 1, 0 , -3/ 10, 0
0 , 1, 11/ 10 , 0,
0 , 0, 0, 1
)
)}}}

so, your solutions ae: , , and