Solve the simultaneous equations:?

Question

a) y^2=1-x^2
3y-4x=0

b) 2/a-5/b-20=0
5/a+2/b-21=0

Answer 1

a)
y^2=1-x^2
y=4x/3

(4x/3)^2=1-x^2
25x^2/9=1
x=±3/5
y=±4/5
Solution: (3/5, 4/5) and (-3/5, -4/5)

Answer 2

a) y^2=1-x^2 ----------------(1)
3y-4x=0 -----------------(2)

from (2),

x = 3y/4 ---------(2a)

subst into (1),

y^2 = 1 - (3y/4)^2

y^2 + 9y^2/16 = 1

y^2 (25/16) = 1

y^2 = 16/25

y = +- 4/5


subst into (2a)

x = +- (3*4)/(4*5)

x = +-3/5


Ans: (x=-3/5, y=-4/5) and (x=3/5, y=4/5)

b) 2/a-5/b-20=0 ----------(3)
5/a+2/b-21=0 ------------(4)

from (3),

2/a = 5/b+20
2/a = (5 + 20b) / b
a = 2b / (5 + 20b) -------(3a)

subst into (4)

5*(5+20b)/2b + 2/b -21 = 0

multiply by 2b....

25 + 100b + 4 - 42b = 0

29 + 58b = 0

b = -1/2 (ans)

subst into (3a),

a = -1 / (5-10)

a = 1/5 (ans)

Answer 3

b) 2/a-5/b-20=0
5/a+2/b-21=0

2b - 5a = 20ab (-2.5)
5b + 2a = 21ab

-5b + 12.5a = -50ab
5b + 2a = 21ab
14.5a = -29ab
a = -29ab/14.5
a = -2

5b + 2(-2) = 21(-2)b
5b - 4 = -42b
-1 -5/b = 20
-5/b = 20 +1
-5 = 21b
b = -5/21
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Answer 4

umm, nonoffense but uh, some ppl either arent learing this or arent in that subjet yet. i think i can only help u with one thing. when numbers and letters together mean to multily.m for b) im guessing... 2/a-5/b-20 is 2/10-5/4-20=0thats the only one i know.i doint know many of this, mainly because im a 6thb grader, but i just somewhat guessed.

Answer 5

a)
y² = 1 -x²
3y - 4x = 0
y = 4x/3
(4x/3)² = 1 - x²
16x² / 9 = 1 - x²
16x² = 9 - 9x²
25x² = 9
x² = 9 / 25
x = ± 3/5
y² = 16/25
y = ± 4/5

set of solution = { (3/5 , 4/5 ) , (-3/5 , -4/5) }
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