Matematické Fórum

postup

Solve the following system:
{a = b+c
(1.+0. i) b+(0.147904-0.0471032 i) c = 0
(0.+6.28 i) a+(10.+31.4 i) c = 220
Perform a substitution.
Substitute a = b+c into the third equation:
{a = b+c
(1.+0. i) b+(0.147904-0.0471032 i) c = 0
(0.+6.28 i) (b+c)+(10.+31.4 i) c = 220
Expand the left hand side of the equation (0.+6.28 i) (b+c)+(10.+31.4 i) c = 220.
(31.4 i+10.) c+(6.28 i+0.) (b+c) = ((0.+6.28 i) b+(0.+6.28 i) c)+(10.+31.4 i) c = (0.+6.28 i) b+(10.+37.68 i) c:
{a = b+c
(1.+0. i) b+(0.147904-0.0471032 i) c = 0
(0.+6.28 i) b+(10.+37.68 i) c = 220
Choose an equation and a variable to solve for.
In the second equation, look to solve for b:
{a = b+c
(1.+0. i) b+(0.147904-0.0471032 i) c = 0
(0.+6.28 i) b+(10.+37.68 i) c = 220
Isolate terms with b to the left hand side.
Subtract (0.147904-0.0471032 i) c from both sides:
{a = b+c
b (0. i+1) = c (0.0471032 i-0.147904)
(0.+6.28 i) b+(10.+37.68 i) c = 220
Solve for b.
Multiply both sides by 1:
{a = b+c
b = c (0.0471032 i-0.147904)
(0.+6.28 i) b+(10.+37.68 i) c = 220
Perform a substitution.
Substitute b = (-0.147904+0.0471032 i) c into the third equation:
{a = b+c
b = (-0.147904+0.0471032 i) c
(9.70419+36.7512 i) c = 220
Choose an equation and a variable to solve for.
In the third equation, look to solve for c:
{a = b+c
b = (-0.147904+0.0471032 i) c
(9.70419+36.7512 i) c = 220
Solve for c.
Divide both sides by 9.70419+36.7512 i:
{a = b+c
b = (-0.147904+0.0471032 i) c
c = -5.59603 i+1.47764
Perform a back substitution.
Substitute c = 1.47764-5.59603 i into the first and second equations:
{a = b+(1.47764-5.59603 i)
b = 0.0450421+0.897277 i
c = 1.47764-5.59603 i
Perform a back substitution.
Substitute b = 0.0450421+0.897277 i into the first equation:
{a = 1.52268-4.69876 i
b = 0.0450421+0.897277 i
c = 1.47764-5.59603 i
Remove extraneous solutions.
No solutions exist:
Answer: | 
| (no solutions)