1. ## Solving 2 unknowns??

Hello,

I have the following equation with two unknowns and I can't seem to solve it.

0.5 = 3.5m + 3d

I made 2 equations (one for each unknown)

Equation for m:
m = (0.5 - 3d)/3.5

Equation for d:
d = (0.5 - 3.5)/3

First, I tried solving for d by substituting m in original equation as:
0.5 = 3.5(m) + 3d

so equation becomes:
0.5 = 3.5( (0.5 - 3d) /3.5) + 3d
0.5 - 3d = 3.5( (0.5 - 3d) /3.5)
0.5 - 3d = 3.5(0.5/3.5 - 3d/3.5)
0.5 - 3d = 3.5(0.5/3.5) - 10.5d/3.5
0.5 - 3d = 0.5 - 10.5d/3.5
0.5 + 0.5 - 3d = 10.5d/3.5
1-3d = 10.5d/3.5
3.5(1-3d) = 10.5d
3.5 - 10.5d = 10.5d
3.5 = 21d
3.5/21 = d
d = 0.166666666 ????

I believe "d" is supposed to equal 1.45 !

2. ## Re: Solving 2 unknowns??

Couple things. First, d = (0.5-3.5m)/3. Second you can not uniquely solve a single equation with two unknowns. You have an "under-determined" system, meaning you have more variables than you have equations. The best you can do is solve one variable in terms of the other, which will in term determine a line containing all solutions to your equation.

3. ## Re: Solving 2 unknowns??

To get a unique solution for a number of variables you need the same number of equations. Even then there is no guarantee that there will be a unique solution though, more analysis would be needed...

4. ## Re: Solving 2 unknowns??

Originally Posted by Prove It
To get a unique solution for a number of variables you need the same number of equations. Even then there is no guarantee that there will be a unique solution though, more analysis would be needed...
Can you please explain or refer me in the direction as to why?

Thanks!

5. ## Re: Solving 2 unknowns??

Using what basis? How much algebra do you know? YOU said that you knew that you can write the equation as m = (0.5 - 3d)/3.5. Can you not see that choosing any value for d gives you a value of m so that m and d satisfy the equation? For example, if d= 1, then m= (0.5- 3)/3.5= -2.5/3.5= -25/35= -5/7. d= 1, m= -5/7 satisfy the equation. Or if you choose d= 2, m= (0.5- 6)/3.5= -5.5/3.5= -55/35= -11/7 so d= 2, m= -11/7 is another pair of numbers that satisfy the equation.

Similarly, YOU said that you could write the equation as d = (0.5 - 3.5m)/3 (you don't have the "m" but you clearly intended that) then if m= 1, d= (0.5- 3.5)/3= -3/3= -1. d= -1, m= 1 satisfy this equation.

I don't know if you have ever learned about graphing equation but if we were to graph 0.5 = 3.5m + 3d, taking m as, say, the horizontal axis and d as the vertical axis, the graph is the straight line through
the points (0, 1/3) and (1/7, 0). Every point on that line corresponds to a (m, d) pair that satisfies the equation.