okay ive got a few questions regarding a maths simultaneous equations
hope u guys can help
question 1:
Find the coordinates of each of the points of intersection of the curve xy=10 and the line 2x + 3y = 16
question 2:
Find the coordinates of the points of intersection of the line x + y = 12 and the curve y = 10/x + x
let me help you.
x = 10/y -------- (1)
2x + 3y = 16 --------- (2)
sub (1) into (2)
2(10/y)+3y = 16 ----- (3)
Multiply each side of (3) by y
20 + 3y^2 = 16y
3y^2-16y+20 = 0 ------- (4)
Factorise (4)
(3y-10)(y-2) = 0
y = 3 1/3 or 2
When y = 3 1/3
x = 10/ (3 1/3) = 3
When y = 2
x = 10/2 = 5
Therefore the coordinates are:
(5, 2) and (3, 3 1/3)
Originally posted by jayh272416:let me help you.
x = 10/y -------- (1)
2x + 3y = 16 --------- (2)sub (1) into (2)
2(10/y)+3y = 16 ----- (3)
Multiply each side of (3) by y
20 + 3y^2 = 16y
3y^2-16y+20 = 0 ------- (4)Factorise (4)
(3y-10)(y-2) = 0
y = 3 1/3 or 2
When y = 3 1/3x = 10/ (3 1/3) = 3
When y = 2
x = 10/2 = 5
Therefore the coordinates are:
(5, 2) and (3, 3 1/3)
and this is for question 1 right?
qn 2
x+y = 12 ----- (1)
y = 10/x + x ----- (2)
Sub (2) into (1)
2x + 10/x = 12 ----- (3)
Multiply each side of (3) by x
2x^2 + 10 = 12x
2x^2 - 12x + 10 = 0
x^2 - 6x + 5 = 0
(x-5)(x-1) = 0
x = 5 or 1
If x = 5,
y = 12-5 = 7
If x = 1,
y = 12-1 = 11
Coordinates are:
(5,7) and (1,11)
Originally posted by SBS7484P:
and this is for question 1 right?
Yeah.
k thanks for the help.. one more.. hold on a sec
Find the coordinates of the points of intersection of the line 2x-y=5 and the curve x^2+xy=2
Originally posted by SBS7484P:Find the coordinates of the points of intersection of the line 2x-y=5 and the curve x^2+xy=2
2x-y=5------(1)
x^2+xy=2-----(2)
From (1)
y = 2x-5 ----- (3)
Sub (3) into (2)
x^2 + x(2x-5) = 2
3x^2-5x-2=0
(3x+1)(x-2)=0
x = -1/3 or 2
when x = -1/3,
y = -5 2/3
when x = 2,
y = -1
coordinates are:
(-1/3, -5 2/3) and (2,-1)
thanks alot. =)
another 25 questions of random coming up.. ah wait. i go make anotehr thred on that.. this title dun seem very app;ropriate
mod pls lock thanks
You're using hw forums to help you do your hw???
He's not even requesting for help, he's asking the forumers to do it for him.
Originally posted by SBS7484P:Find the coordinates of the points of intersection of the line 2x-y=5 and the curve x^2+xy=2
2x - y - 5 = 0 ------------ (Equation 1)
x^2 + xy - 2 = 0 ----------- (Equation 2)
Multiply (Equation 1 ) by x and hence:
2x^2 - xy - 5x = 0 ............. (Let's call it Equation 3)
Add Equation 3 to Equation 1:
(2x^2 + x^2) + (-xy + xy) - 5x - 2 = 0
--------> 3x^2 - 5x -2 = 0
Now you should be able to factorise it. It should have 2 coordinates (x1, y1) and (x2, y2).
Lol, is HWF helping him or harming him XD
Originally posted by SBS7484P:okay ive got a few questions regarding a maths simultaneous equations
hope u guys can help
question 1:
Find the coordinates of each of the points of intersection of the curve xy=10 and the line 2x + 3y = 16
xy=10
x=10/y -- (1)
2x + 3y = 16 --(2)
Sub (1) into (2): 20/y + 3y = 16
20 + 3y^2 =16y
3y^2-16y+20 = 0
(3y-2)(y-10) = 0
y = 2/3 OR y=10
Sub y=2/3 and y=10 into (2)
2x + 2 = 16 OR 2x + 30 = 16
x = 7 x = -7
Therefore the coordinates are (7, 2/3) and (-7, 10).