Simultaneous equation

[vanhelsingh]

Can't seem to solve it:
http://img258.imageshack.us/img258/377/mathsug1.png

[Logophobic]

y - 2x = 3
y = 2x + 3
y2 = (2x + 3)2

[NickThissen]

y - 2x = 3
y = 2x + 3

--> submit y into second equation:
x² + y² = 18
x² + (2x + 3)² = 18
etc... (you only have x left now)

Then, when you get x (both of them), submit them into either one of the equations to get y aswell.

[extreme.aly]

let me solve this...

y - 2x = 3
y = 2x + 3

--> submit y into second equation:
x² + y² = 18
x² + (2x + 3)² = 18
x² + ([2x]² + 2[2x][3] + [3]²) = 18
x² + (4x² + 12x + 9) = 18
x² + 4x² + 12x + 9 = 18
5x² + 12x + (9 - 18) = 0
5x² + 12x - 9 = 0
Now put them in quadratic formula (-b √[b² - 4 a c]) / [2a]
a = 5, b = 12, c = -9

[opus]

It was OK until:let me solve this...

y - 2x = 3
y = 2x + 3

--> submit y into second equation:
x² + y² = 18
x² + (2x + 3)² = 18
x² + ([2x]² + 2[2x][3] + [3]²) = 18
x² + (4x² + 12x + 9) = 18
x² + 4x² + 12x + 9 = 18
5x² + 12x + (9 - 18) = 0
5x² + 12x - 9 = 0

Now try again

[extreme.aly]

there are 3-4 ways to solve this equation...
1.quadratic formula
2.completing the square (the most difficult)
3.breaking the middle term..
4. i forgot that one or maybe there are only 3...

we will use the first one which is easy to use in scriptings...

the formula is:
____________
-b ±√ b² - 4*a*c
-------------------- <--- divide sign
2*a
this is the formula... now we got 5x² + 12x - 9 = 0 in the end
we will suppose a,b,c like this:

5x² + 12x - 9 = 0
ax² + bx + c = 0 so we got:
a=5, b=12, c=-9

now put these values in that formula
____________
-b ±√ b² - 4*a*c
-------------------- <--- divide sign
2*a
====================================
________________
-(12) ±√ (12)² - 4*(5)*(-9)
---------------------------- <--- divide sign
2*(5)
====================================
___________
-12 ±√ 144 - (-180) (4*5 = 20, 20*-9 = -180)
---------------------------- <--- divide sign
2*(5)
====================================
_________
-12 ±√ 144 + 180 (minus * minus = plus)
------------------ <--- divide sign
2*(5)
====================================
____
-12 ±√ 324
---------- <--- divide sign
10
====================================
-12 ±18 (square root of 328 is 18)
---------- <--- divide sign
10
====================================
now we will get two values of x: look below:
-12 +18 -12-18
---------- AND ---------
10 10
==========================
6 -30
--- AND ----
10 10
===============
3 -3
--- AND ---
5 1
==================
so,
x= 3/5 and x= -3

[extreme.aly]

now as you've got 2 values of 'x'... so you will get two values of 'y' also...:
y = 2x + 3 (see MY first post to know that how this comes)

x = (3/5) or 0.6 <---(value 1) put this value in 'y' (above)

y = 2x + 3
y = 2(0.6) + 3
y = 1.2 + 3
y = 4.2 (value 1) this become (0.6, 4.2) co-ordinates

x = -3 (value 2)
put this value in 'y'
y = 2x + 3
y = 2(-3) + 3
y = -6 + 3
y = -3 (value 2) coordinates: (-3, -3)

Don't forget to rate my post if this helps you!!!!