Answer:
1. x = 5, y = 13/2
2. x = 15 , y = 24
Explanation:
Solve the following system:
{8 y + 6 x = 82 | (equation 1)
{6 y + 9 x = 84 | (equation 2)
Swap equation 1 with equation 2:
{9 x + 6 y = 84 | (equation 1)
{6 x + 8 y = 82 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{9 x + 6 y = 84 | (equation 1)
{0 x + 4 y = 26 | (equation 2)
Divide equation 1 by 3:
{3 x + 2 y = 28 | (equation 1)
{0 x + 4 y = 26 | (equation 2)
Divide equation 2 by 2:
{3 x + 2 y = 28 | (equation 1)
{0 x + 2 y = 13 | (equation 2)
Divide equation 2 by 2:
{3 x + 2 y = 28 | (equation 1)
{0 x + y = 13/2 | (equation 2)
Subtract 2 × (equation 2) from equation 1:
{3 x + 0 y = 15 | (equation 1)
{0 x + y = 13/2 | (equation 2)
Divide equation 1 by 3:
{x + 0 y = 5 | (equation 1)
{0 x + y = 13/2 | (equation 2)
Collect results:
Answer: {x = 5, y = 13/2
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Solve the following system:
{8 y + 3 x = 237 | (equation 1)
{3 y + 5 x = 147 | (equation 2)
Swap equation 1 with equation 2:
{5 x + 3 y = 147 | (equation 1)
{3 x + 8 y = 237 | (equation 2)
Subtract 3/5 × (equation 1) from equation 2:
{5 x + 3 y = 147 | (equation 1)
{0 x + (31 y)/5 = 744/5 | (equation 2)
Multiply equation 2 by 5/31:
{5 x + 3 y = 147 | (equation 1)
{0 x + y = 24 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{5 x + 0 y = 75 | (equation 1)
{0 x + y = 24 | (equation 2)
Divide equation 1 by 5:
{x + 0 y = 15 | (equation 1)
{0 x + y = 24 | (equation 2)
Collect results:
Answer: {x = 15 , y = 24