simultaneous equations

SBS7484P SG

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

SBS7484P SG

question 2:

Find the coordinates of the points of intersection of the line x + y = 12 and the curve y = 10/x + x

jayh272416 SG

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)

SBS7484P SG

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)

and this is for question 1 right?

jayh272416 SG

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)

jayh272416 SG

and this is for question 1 right?

Yeah.

SBS7484P SG

k thanks for the help.. one more.. hold on a sec

SBS7484P SG

Find the coordinates of the points of intersection of the line 2x-y=5 and the curve x^2+xy=2

jayh272416 SG

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)

SBS7484P SG

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

fairlady_xoxo SG

You're using hw forums to help you do your hw???

Gosu. SG

He's not even requesting for help, he's asking the forumers to do it for him.

honeymouse SG

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).

CreativeMaggot SG

Lol, is HWF helping him or harming him XD

MrSean SG

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).