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4 years ago

Solve the system and give your answer as a coordinate point in the form (k, c) k+c=100 51k+11c=2500

Mathematics

1 answer:

Aleks [24]4 years ago

5 0

Answer:

k = 35, c = 65

Step-by-step explanation:

Solve the following system:

{c + k = 100 | (equation 1)

{11 c + 51 k = 2500 | (equation 2)

Swap equation 1 with equation 2:

{11 c + 51 k = 2500 | (equation 1)

{c + k = 100 | (equation 2)

Subtract 1/11 × (equation 1) from equation 2:

{11 c + 51 k = 2500 | (equation 1)

{0 c - (40 k)/11 = -1400/11 | (equation 2)

Multiply equation 2 by -11/40:

{11 c + 51 k = 2500 | (equation 1)

{0 c+k = 35 | (equation 2)

Subtract 51 × (equation 2) from equation 1:

{11 c+0 k = 715 | (equation 1)

{0 c+k = 35 | (equation 2)

Divide equation 1 by 11:

{c+0 k = 65 | (equation 1)

{0 c+k = 35 | (equation 2)

Collect results:

Answer: {c = 65 , k = 35

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