How to solve "2x+2y=22, xy=30?

Answer 1

2(x+y)=22
dividing by 2
x+y=11
xy=30
y=30/x
30/x+x=11
30+x^2=11x
x^2-11x+30=0
(x-6)(x-5)=0
x=6 or 5
sub y=6 if x=5 and y=5 if x=6

Answer 2

You have 2x+2y=22, xy=30
xy=30 => x=30/y
Substituting in 2x+2y=22 we get
2(30/y) + 2y = 22
=>(60/y) + 2y = 22
=>(60) + 2y^2 = 22y
=>2y^2 - 22y +60 = 0
=>y^2 - 11y + 30 = 0
=>y^2 - 6y - 5y + 30 = 0
=>y(y - 6) - 5(y -6) = 0
=>(y - 6)(y -5) = 0
=>(y - 6)=0 or(y -5) = 0
=>y = 6 or y = 5

So, x=30/y implies
x=30/6 = 5 or x=30/y = 30/5 = 6

S0, the solutions are (5,6) or (6,5)

Answer 3

2x² +2y² = 22- - - - - - Equation 1
xy = 30- - - - - - - - - - Equation 2
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Substitute Method equation 2

xy = 30

y = 30/x

Insert the y value into equation 1

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Solving for x

2x + 2y = 22

2x + 2(30/x) = 22

2x + 60/x = 22

x(2x) + x(60x) = x(22)

2x² + 60 = 22x

2x² + 60 - 22x = 22x - 22x

2x² - 22x + 60 = 0

2(x² - 11 + 30) = 0

2(x - 6)(x - 5) = 0

x = 6

x = 5

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Solving for y

2x + 2y = 22

2(6) + 2y = 22

12 + 2y = 22

12 + 2y - 12 = 22 - 12

2y = 10

2y/2 - 10/2

y = 5

The answer is y = 5

Insert the y value into equation 1

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Check for equation 1

2x + 2y = 22

2(6) + 2(5) = 22

12 + 10 = 22

22 = 22

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Check for equation 2

xy = 30

(6)(5) = 30

30 = 30

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The solution set is { 6, 5 }

Using x = 5 changes the y value to y = 6 both values of x works.

- - - - - - s-

Answer 4

this is wat u call a simultaneous equation

2x + 2y = 22
we can take 2 common to mek life easier
2 (x + y) = 22
x + y = 22 / 2
x + y = 11
therefore x = 11 - y

subsituting x in the other equation, we get
xy = 30
or (11-y)y = 30
11y - y^2 = 30
or if we took the terms on the left to the right so as to make the y^2 positive, it wud be

y^2 - 11y + 30 = 0
now its a simple quadratic equation
y^2 - 6y - 5y + 30 = 0
y(y-6) - 5(y-6) = 0
(y-6) (y-5) = 0
therefore, y = 6, y = 5
now u hav to substitute each value of y in any equation separately so as to find x
u will get 4 answers in all, two for y and two for x

i think when y = 6
x = 5
and wen y = 5
x = 6

Answer 5

First divide both sides of the first equation by 2, to get
x + y = 11.

Now, since the second equation tells us that xy = 30, it would be good to have xy in the first, so multiply both sides by x, and then replace xy by 30.

You now have a quadratic equation which I hope you can solve to find x, then find y since x+y = 11.

And of course the solution given by Nisha and Gopal is correct, and is a bit more general. Mine depends on noticing something a bit special about these two equations.

I like Vasa's "by inspection", because the truth is that if you try to solve the quadratic by factors, you are looking for two numbers whose product is 30 and whose sum is 11, which is just what the two equations say.

Answer 6

I'm not sure,but i read the answer to my Math Book:
2x+2y=22, xy=30
Answers:
2[x+y]=22 you must divide it by 2
x+y=11
y=30/x
30/x+x=11
30+x^2=11x
x^2-11x+30=0

CAN YOU DO THE REST,IT'S NOT ON MY BOOK
GOOD LUCK !

Answer 7

From all the good answers given above, now you know how to arrive at the quadratic equation namely,

X^2-11X+30=0.

But while solving this quadratic equation, one has to find two numbers whose sum is eleven and product is thirty. This is usually done by trail and error method.

Normally we don’t use the formula {-b (+ or -) square root of bb- 4ac}/2a to find the solution.

Therefore, read the problem once again.

It is given that sum of two numbers is eleven and their product is thirty.

The answer is got by trial and error method to be six and five.
I repeat you will be doing the same when solving the quadratic equation.

If one is interested only in the answer then the lengthy algebraic equations are not at all needed and they are all superfluous and the problem ends to the beginning.

Answer 8

We have x+y = 11 and xy = 30

This gives us x+30/x = 11

or x^2 -11x + 30 = 0

Which gives x = 5 or 6

which means y = 6 or 5

Answer 9

2x+2y=22
x+y=11
x=11-y
Substitute value of y in xy
11y-y*y=30
Then solve using splitting the middle term
The answer is that either x=5 & y=6 or y=5 & x=6
You can also solve by using quadratic formula

Answer 10

2(x+y) = 22
x+y=11

x.y=30 y=30/x

x+30/x=11

x^2 +30=11x

x^2-11x+30=0
(x-5) (x-6)= 0
X-5=0 x-6=0

x=5 or X=6

both of them supply equality and y=5 or 6