solve(cross multiplication)
2x/3+3y/5=17
3x/4+2y/3=19

Dear student

t h e g i v e n s y s t e m o f e q u a t i o n s i s \frac{2 x}{3} + \frac{3 y}{5} - 17 = 0 \frac{3 x}{4} + \frac{2 y}{3} - 19 = 0 B y c r o s s - m u l t i p l i c a t i o n, w e g e t \frac{x}{[\frac{3}{5} \times (- 19)] - [\frac{2}{3} \times (- 17)]} = \frac{- y}{[\frac{2}{3} \times (- 19)] - [\frac{3}{4} \times (- 17)]} = \frac{1}{[(\frac{2}{3} \times \frac{2}{3}) - (\frac{3}{4} \times \frac{3}{5})]} \frac{x}{\frac{- 57}{5} + \frac{34}{3}} = \frac{- y}{\frac{- 38}{3} + \frac{51}{4}} = \frac{1}{\frac{4}{9} - \frac{9}{20}} \frac{x}{\frac{- 1}{15}} = \frac{- y}{\frac{1}{12}} = \frac{1}{\frac{- 1}{180}} \Rightarrow \frac{x}{\frac{- 1}{15}} = \frac{1}{\frac{- 1}{180}} \Rightarrow 15 x = 180 \Rightarrow x = 12 a n d \Rightarrow \frac{- y}{\frac{1}{12}} = \frac{1}{\frac{- 1}{180}} \Rightarrow 12 y = 180 \Rightarrow y = 15

Regards

solve(cross multiplication) ​2x/3+3y/5=17 3x/4+2y/3=19