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# Simultaneous equation

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5x + 2y = 22
10x + 9y =59

What is the value of x & y ?
Jun 10, 2017

### 1+0 Answers

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Solve the following system:
{5 x + 2 y = 22 | (equation 1)
10 x + 9 y = 59 | (equation 2)
Swap equation 1 with equation 2:
{10 x + 9 y = 59 | (equation 1)
5 x + 2 y = 22 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{10 x + 9 y = 59 | (equation 1)
0 x - (5 y)/2 = (-15)/2 | (equation 2)
Multiply equation 2 by -2/5:
{10 x + 9 y = 59 | (equation 1)
0 x+y = 3 | (equation 2)
Subtract 9 × (equation 2) from equation 1:
{10 x+0 y = 32 | (equation 1)
0 x+y = 3 | (equation 2)
Divide equation 1 by 10:
{x+0 y = 16/5 | (equation 1)
0 x+y = 3 | (equation 2)
Collect results:
Answer: | x = 16/5         and            y = 3

Jun 10, 2017

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