# Can we do this?

1. Sep 13, 2006

### mubashirmansoor

can we do this???

Can we solve 3 variables with 2 points? like this one

4a+2b+c=4
a+b+c=1

can we get the numerical values of all 3 variables???

2. Sep 13, 2006

### HallsofIvy

Staff Emeritus
No. If you think of a, b, c as the x,y,z components of a point in 3 dimensional space, the 2 equations are equations of planes. The two equations will be satisfied for points where the two planes intersect. Two planes either are parallel and so don't intersect (so there is no solution) or intersect in a line (so there are an infinite number of solutions). But there cannot be a case where two planes intersect in a single point.

3. Sep 17, 2006

### murshid_islam

subtract the 2nd eqn. from the 1st one and you get:
3a + b = 3
or, b = 3 - 3a

here putting different values of a, you can get different values of b. and then putting those values of a and b in either one of the original equations, you can get the value of c. thus, you can get and infinite number of solutions.

for example, if a = 1, then
b = 3-3a = 3-3*1 = 0 and
c = 1-a-b = 1-1-0 = 0
so, one solution is (a,b,c) = (1,0,0)

4. Sep 17, 2006

### matt grime

By inspection you can see there is no unique answer.

5. Sep 17, 2006

### murshid_islam

of course we can. i was not sure whether mubashirmansoor wanted only unique answers. i thought he might have wanted a number of solutions (like the solutions of a diophantine equations).