Simultaneous equation

[vanhelsingh]

Can't seem to solve it:

[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!!!!