Question

3x-2y=1/2(2x-y)
1/2(5x-4y)=1/3(4x-3)​

Answer 1

$SOLUTION :—$

$3x - 2y = \frac{1}{2} (2x - y) \: \: \: \: \: \: \: \: \: \: \: \: \: ...equation \: 1\\ \frac{1}{2} (5x - 4y) = \frac{1}{3} (4x - 3) \: \: \: \: \: \: \: \: \: ....equation \: 2$

$=>\: \: 3x - 2y = x - \frac{1}{2} y \\ =>3x - x = - \frac{1}{2} y + 2y \\ =>2x = \frac{4y}{2} - \frac{y}{2} \\ => \:2x = \frac{3y}{2 } \\ =>x = \frac{3y}{4} \: \: \: \: \: \: \: \: \: ....(equation \: 1)$

$NOW \: EQUATION \: 2$

$\frac{1}{2} (5x - 4y) = \frac{1}{3} (4x - 3) \\ => \frac{5x}{2 } - 2y = \frac{4x}{3} - 1 \\ => \frac{5x}{2} - \frac{4x}{3} = 2y - 1 \\ => \frac{15x - 8x}{6} = 2y - 1 \\ => \frac{7x}{6} = 2y - 1 \\ =>x = \frac{6}{7} (2y - 1) \\ =>x = \frac{12y}{7} - \frac{6}{7}$

$NOW, SUBSTITUTING \: BOTH \: THE \: EQUATION —$

$\frac{3y}{4 } = \frac{12y}{7} - \frac{6}{7} \\ => \frac{3y}{4} - \frac{12y}{7 } = \frac{ - 6}{7 } \\ => \frac{21y - 48y}{28} = \frac{ - 6}{7} \\ => \frac{ - 27y}{28} = \frac{ - 6}{7} \\=>y = \frac{ - 6}{7} \times \frac{ 28}{ - 27} \\ =>y = \frac{8}{9}$

$NOW \: SUBSTITUTING \: THE \: \: VALUE \: OF \: Y, AND \: GETTING$

$THE \: \: VALUE \: OF \: X —$

$3x - 2y = \frac{1}{2} (2x - y) \\ =>x = \frac{3y}{4} \\ =>x = \frac{3 \times \frac{8}{9} }{4 } \\ =>x = \frac{8}{3} \times \frac{1}{4} \\=>x = \frac{2}{3}$

$Hence, \: x = \frac{2}{3} , \: y = \frac{8}{9} \\ \\ hope \: it \: helps \: you$