Question

Solve for x and y:
(i)   y + 7/5 = 2y - x/4 + 3x - 5
      7- 5x/2 + 3 - 4y/6 = 5y - 18

(ii)   34/3x + 4y + 15/3x - 2y = 5
       25/3x - 2y - 8.50/3x + 4y = 4.5

Answer 1

1)
$y + \frac{7}{5} = 2 y - \frac{1}{4}x + 3 x - 5,\ \ \ = > 2y-y+\frac{3*4-1}{4}x-5-\frac{7}{5}=0\\==> y+\frac{11}{4}x-\frac{5*5-7}{5}=0,\ \ == > 20y + 11x-72=0,\ \ -- equation1\\ \\7-\frac{5}{2}x+3-\frac{2}{3}y=5y-18,\ \ \ \frac{3*5+2}{3}y+\frac{5}{2}x-18-7-3=0\\ \\== > 34y+15x-168=0 -- equation2$

Multiply  equation 1 by 17 and subtract equation 2 * 10 ==>

340 y + 187 x - 72*17 - 340 y - 150 x + 1680 = 0
x = 456/37    y = [ 72 - 11* 456 / 37 ] / 20

2)  

$\frac{34}{3}x+4y+\frac{15}{3}x-2y=5,\ \ \ == > \frac{49}{3}x+2y=5,\ \ => 49x+6y=15\\ \\\frac{25-8.5}{3}x-2y+4y=9/2,\ \ == > \frac{16.5}{3}x+2y=\frac{9}{2},\ == > 33x+12y=27$

Multiply equation 1 by 2 and subtract equation 2,

98 x + 12 y - 33x - 12 y = 30 - 27 
65 x = 3 

x = 3 / 65

y = [ 15 - 49 * 3/65 ] / 6

Answer 2

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