Solve the following pair of equations : $\displaystyle \frac{3}{5}x-\displaystyle \frac{2}{3}y+1= 0$ $\displaystyle \frac{1}{3}y+\displaystyle \frac{2}{5}x= 4$

Multiplying the first equation by 15 gives 9x - 10y = -15. Multiplying the second equation by 15 gives 6x + 5y = 60. Multiplying this second result by 2 gives 12x + 10y = 120. Adding this to the first result yields 21x = 105, so x = 5. Substituting x = 5 into 6x + 5y = 60 gives 30 + 5y = 60, so y = 6. The solution is x = 5, y = 6.

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