1. simultaneous equation

hi i asked about this yesterday but didn't get the help i was looking for exactly. could someone tell me how to figure out 12x + 65y - 1 = 0 and 60y = 150x + 511. i mean could you show how you would figure it out from start to finish with all the workings out. cheers

2. Originally Posted by mark
hi i asked about this yesterday but didn't get the help i was looking for exactly. could someone tell me how to figure out 12x + 65y - 1 = 0 and 60y = 150x + 511. i mean could you show how you would figure it out from start to finish with all the workings out. cheers
Hi mark,

You have the option of solving this system using a variety of methodologies. But, I would expect you are limited to, say, elimination or substitution method, right?

$\displaystyle 12x+65y-1=0$

$\displaystyle 60y=150x+511$

For this system, I would suggest that we put each equation in the form:

$\displaystyle ax + by = c$ and use the elimination method. It just seems like it's better suited for this method over the substitution method.

(1) $\displaystyle 12x+65y=1$

(2) $\displaystyle 150x-60y=-511$

With this arrangement, let's eliminate the x-value by multiplying the (1) equation by 25 and the (2) equation by -2.

You see, I found out that the LCM of 12 and 150 was 300, and that helped me make the decision to go with elimination.

(1)$\displaystyle 300x+1625y=25$

(2)$\displaystyle -300x+120y=1022$

Now add (1) + (2) = (3)

(3) $\displaystyle 1745y=1047$

(3) $\displaystyle {\color{red}y=\frac{3}{5}}$

Now use this y-value to substitute into (1) to discover the x-value.

(1) $\displaystyle 12x+65\left(\frac{3}{5}\right)=1$

$\displaystyle 12x+39=1$

$\displaystyle 12x=-38$

$\displaystyle {\color{red}x=-\frac{19}{6}}$

You can check these answers by substituting them back into each of the original two equations.

3. Hi, I hope this helps.

You have 12x + 65y - 1 = 0 and 60y = 150x + 511.

Rearrange them and you get:
12x+65y=1 --(1)
300x+1625y=25 --(2) [this equation (2) is equation (1) multiplied by 25]

150x-60y=-511 --(3)
300x-120y=-1022 --(4) [this equation (4) is equation (3) multiplied by 2]

*the equations in blue are your original equations.

By elimination method, equate (2) and (4) together to get rid of the 300x they have in common:

What's left will be 1625y-(-120y)=25-(-1022)
1745y=1047
y=1047/1745
= 0.6 or 3/5

substitute y=0.6 into any of the equations to get x. For me, I chose equation (1) as it is simpler:

12x+65(0.6)=1
12x+39=1
12x=1-39
12x=-38
x=-38/12
= -19/6

Hence, x=-19/6 and y= 3/5.

4. thanks a lot leo and masters, i understand now