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How do you solve this problem: x-3y=17
2x+y=17?
What is the distance formula?
ANSWER:
x - 3y = 17-----------------------------(1)
2x + y = 17------------------------------(2)
We have different methods to solve such problem.
One of them is elimination method.
For that consider equations 1 and 2
First step is to make coefficient of any of the two variable same.
here we have x and 2x.
so multiply the first equation by 2 so that the coefficient of x becomes 2.
==> 2(x - 3y )= 2*17
Remove the parenthesis,
==> 2*x - 2*3y = 34
==> 2x - 6y = 34----------------------(3)
Now consider equation (2) and (3)
2x - 6y = 34----------------------(3)
2x + y = 17------------------------------(2)
Subtract (2) from (3){ That means subtract left side and right side seperately)
==>2x - 6y - (2x + y) = 34 -17
==>2x - 6y - 2x - y) = 17
==> - 7y = 17
Divide -7 on both sides of the equation
==> - 7y/-7 = 17/7
==> y = 17/7
Now substitute this value in any one of the given equations.
Let's take the second equation,
2x + (- 17/7 )= 17
2x - 17/7 = 17
Add 17/7 from both sides of the equation.
2x -17/7 + 17/7 = 17 + 17/7
2x = 136/7
Divide both sides by 2
==> 2x/2 = 136/2*7
==> x = 68/7
So the required solution is,
x = 68/7 and
y = -17/7
(You can chek this answer by plugging these values in the given equation.)
Hope you understood.
DISTANCE FORMULA:
In algebraic geometry, one can find the distance between two points of the xy-plane using the distance formula. The distance between (x1, y1) and (x2, y2) is given by
d = square root of { (x1 - x2)^2 + ( y1 - y2 ) ^2}
For example,
If A ( 5, 7 ) and B( -1 , 15 )
then by distance formula, the distance betweeen A and B is given by,
d = square root of { (x1 - x2)^2 + ( y1 - y2 ) ^2}
d = square root of { (5 - -1)^2 + ( 7 - 15 ) ^2}
d = square root of { (6)^2 + ( -8 ) ^2}
d = square root of { 36 + 64 }
d = square root of { 100 }
d = 10
That is distance between the points A ( 5, 7 ) and B( -1 , 15 ) is 10 units.
Hope you understood.
Regards,
praseenakos@yahoo.co.in
