how do i solve this equation ?
i get how 2 do the substitution and all but i cant solve this
its different the proble is:
f = 6 - 2g
1/6f + 1/3g = 1
do i just use that f or what ?
2006-10-11 09:10:26 · 10 answers · asked by Jan 2 in Science & Mathematics ➔ Mathematics
Normally, you could just use your expression for f to rewrite the second equation as (1/6)(6 - 2g) + (1/3)g = 1. Multiply it out to get 1 - g/3 + g/3 = 1 ==> 1 = 1, a simple true statement. What this means is that the two equations you started with were not linearally independent, so there are actually an infinite number of solutions.
2006-10-11 09:12:38 · answer #1 · answered by DavidK93 7 · 1⤊ 0⤋
Normally, you can subsitute f=6-2g into the second question, and then you have one equation for g that you can solve. That's what they're referring to as "substitution".
The problem with this particular system is that the two equations are not independent of one another. Once you substitute, you get 1=1. You need another equation, that is not a multiple of these, in order to determine f and g.
2006-10-11 09:14:05 · answer #2 · answered by James L 5 · 1⤊ 0⤋
The simplest way to see what's going on here is to multiply the 2nd equation by 6 which gives you f+2g=6 which is a rearranged form of the 1st equation.
This means that in graphical terms these equations are for the same line! This means that there are an infinite number of solutions-every point on the line gives a solution!
2006-10-11 09:18:01 · answer #3 · answered by Gina7 1 · 1⤊ 0⤋
yes substitute 6-2g into f
(6-2g)/6 + g/3 = 1
1 - g/3 + g/3 = 1
solution: identity- any number will work for f
2006-10-11 09:22:14 · answer #4 · answered by stop12345now 2 · 1⤊ 0⤋
I will give you the solution
f+2g=6
take LCM for second equation,you will get 6 so the second equation becomes
f+2g=6
Since the two equations are same you will get infinite values for f and g.
2006-10-11 09:14:12 · answer #5 · answered by Eshwar 5 · 1⤊ 0⤋
First, you resolve for x in the 1st equation. so which you get x= -3y-3. Then, plug in "-3y-3" for x in the 2d equation. You get : 9y= -3(-3y-3) - 9. Then resolve for y. you need to get: 9y=9y. This tells you that there is not any answer to the equation and that's your answer :). the answer does no longer exist.
2016-12-08 12:59:35 · answer #6 · answered by girardot 4 · 0⤊ 0⤋
yea, just use that f
1/6(6-2g) + 1/3g=1
1-1/3g + 1/3g=1
1=1 ohh
The answer is ALL Numbers
2006-10-11 09:14:58 · answer #7 · answered by good answers bad questions 2 · 1⤊ 0⤋
f = 6 - 2g
1/6f + 1/3g = 1 multiply each term by 6fg
g+2f=6fg substitute f=6-2g
g+2(6-2g)=6g(6-2g)
g+12-4g=36g-12g^2
12g^2+g-4g-36g+12=0
12g^2-39g+12=0 divide by 3
4g^2-13g+4=0
g=(13+/-sqrt(169-4*4*4))/8=(13+/-sqrt(105))/8
g=.3441 f=6-2*.3441=5.3118
g=2.906 f=6-2*2.906=.184
f=6-2g
2006-10-11 09:22:08 · answer #8 · answered by yupchagee 7 · 0⤊ 1⤋
both the equations are one and the same/coincidental
so the no of solutions is infinite
2006-10-11 09:18:54 · answer #9 · answered by raj 7 · 0⤊ 1⤋
sure
2006-10-11 09:14:39 · answer #10 · answered by Anonymous · 1⤊ 0⤋