solve 9x^2+25y^2=225 and x^2+y^2=16 simultaneously.?

Answer 1

9x²+25y² = 225 (1)
x²+y² = 16 (2)
multiply (2) by -9

-9x²-9y² = -144 (3)

add (1) and (3)

9x²+25y² = 225
-9x²-9y² = -144
----------------------
16y² = 81
y² = 81/16

substitute y² = 81/16 in (2)
x² + 81/16 = 16
x² = 16 - 81/16
x² = (256 - 81) /16
x² = 175/16
~~~

Answer 2

x^2 +y^2=16.
x^2= 16-y^2.
Substituting for X^2 in the eq 9x^2 +25y^2 =225.

9 ( 16 -y^2) +25y^2 =225.
144- 9y^2 +25Y^2 =225.
16y^2= 225- 144= 81.
y^2 =81/16. y= 9/4substituting the value of y=9/4 in x^2 +y^2=16.
x^2 + 81/16=16.
x^2= 16- 81/16. (256-81)/16= 175/16
x= 5/4 (squareroot of 7). y= 9/4.

Answer 3

9x²+25y² = 225 ----(1)
x²+y² = 16 ----(2)

solve ----(2)
x²= 16 -y² ----(3)

substitute (3) into (1)
9 (16 - y² ) + 25y² = 225
144 - 9y² +25y² = 225
16y² = 81
y² = 81/16
y = 2.25

substitute y² = 81/16 into (2)
x² + 81/16 = 16
x² = 16 - 81/16
x² = (256 - 81) /16
x² = 175/16
x =3.307

Answer 4

well, lets make the equations numbered:
9x^2+25y^2=225-----(1)
x^2+y^2=16------(2)
from 2 we know:
x^2=16-y^2
input this value in 1 to get:
9(16-y^2)^2+25y^2=225
remember the equation (a+b)^2=a^2+2ab+b^2
in this case, a=16 and b=y^2. so:
9(16^2-32y^2-y^2^2)+25y^2=225
2304-288y^2-9y^4+25y^2=225
-263y^2-9y^4=225-2304
and then solve 4 y
input this value in 1.
solve 4 x

Answer 5

Think of at as two linear equations in the two variables x^2 and y^2. You know how to solve those, and the last step of actually finding x and y is of course trivial if you know x^2 and y^2.

A couple of the answers above have already worked that out for you.

You'll get similar problems with the same idea when you take trig.

Answer 6

y^2 = 16-x^2
So substitute this in 1st equation getting:
9x^2 +25(16-x^2) = 225
-16x^2 = -175
x^2 = 175/16
x = +/- 1.25sqrt(7)
y^2 = 16- 175/16 = 81/16
y = +/- 9/4

Answer 7

You can't, philosophically speaking. You can only function on one thing at a time. Even if you solved one, and then the other 1/1000000th of a second later, this is still not simultaneous.

However, if you solved one sub consciously, and the other consciously, you may well do it. Think driving and talking. One is conscious, the other is sub conscious.

But, as you would need to actually put conscious effort into both your equations, you physically cannot solve them simultaneously, in a literal sense.

Answer 8

Basically you solve one equation to get all x on one side and y on the other to get x^2 on the x side, then replace the x^2 on the other equation with the right side and solve.

Answer 9

The order of operations is: Parentheses, Exponents, Multiplication, branch, Addition, Subtraction you are able to submit to in suggestions it by potential of this asserting: PEMDAS- Please Excuse My expensive Aunt Sally SO first you do Exponents. 9squared is 80 one so rewrite the difficulty as... 80 one - 30x = -25 you go with to get the X by potential of itself. so which you will subtract 80 one from the two facets. in case you do something on one area you may do it to the different. 80 one -30x = -25 -80 one -80 one ----------------------- -30x = -106 you go with to proceed to get the x by potential of itself, and -30x potential -30 situations x. you go with to divide by potential of -30 on the two facets to cancel that out! so... -30x = -106 ------- ------- -30 -30 the two thirtys cancel out and pass away X by potential of itself. Now divide -106/-30 and get your answer for the best area of the equivalent sign. X = 3.53333333333333333333333333333333 ( the three repeats)

Answer 10

what grade are you in
and what does ^ mean