Substitution Method
Solve 2x+y=35 and 3x+4y=65 hence find the value of x/y
2x+y=35 —-(i)
3x+4y=65 —-(ii)
From Equation (i) we get,
y= 35-2x —-(iii)
Substituting the value of y in equation (ii) we get,
3x+4(35-2x) =65
⟹ 3x+140-8x=65
⟹ 140-5x=65
⟹ 140-65= 5x
⟹ 75 =5x
⟹ x =$\frac{75}{5}$
⟹ x=15
From equation (iii) we get,
y=35-2(15)
⟹ y=35-30
⟹ y= 5
Therefore Required Solutions are x=15 , y=5
$\therefore \frac{x}{y} = \frac{15}{5} = 3$ [Ans]
Elemination Method
2x+y=35 —(i)
3x+4y=65 —(ii)
Multiplying Equation (i) by 4 we get,
8x +4y=140 —(iii)
Now Subtracting Equations (iii) and (ii) we get,
(8x+4y) -(3x+4y)=140-65
⟹ 8x+4y -3x -4y = 75
⟹ 5x=75
⟹ x = $\frac{75}{5}$
⟹ x = 15
Now from equation (ii) we get,
3(15)+4y=65 [ x =15]
⟹ 45 +4y =65
⟹ 4y=65-45
⟹ 4y=20
⟹ y= $\frac{20}{4}$
⟹ y = 5
Therefore Required Solutions are x=15 , y=5
$\therefore \frac{x}{y} = \frac{15}{5} = 3$ [Ans]