Thread: Equation with 3 unknow

hi all

my question is;

A,B and C is one-digit number different from 0 and each other

200A+40B+10A²+AB+90C=2600

Actually the extended form was

300A+40B=2000
10A²+AB-10C=300
100C-100A=300

but i think both form are sameway or i dont know if there any difference between that two forms about simplicity

Solve for A,B and C

Thanks and best regards.

PS:it would be so good if possible explanation of choice of solution way

The first equation gives 30 A + 4B = 200 OR B = 50 - 15/2 A ---- (1)
the third equation gives C-A = 3 OR C = A + 3 ----- (2)
Since the values of A, B and C is one digit and that too different from each other and zero we can conclude that A should be even. Trying the single digit evens that is 2,4,6,8 we get: for A = 2 , B = 35; A = 4, B = 15; A= 6, B = 5 and for A = 8 we get B = -10. So the only possible value for A is 6 and that gives B as 5 and from equation (2) we get C = 9.
Thus we have, A=6, B=5, C=9. and these values satisfy the third equation.

thank you sir i forgot to say they are positive also but anyway you answerd thanks