Question

find the general solution of 70x + 112y = 168

Answer 1

Answer:

x₁=(-4-8t)

y₁= 4+5t

Step-by-step explanation:

70x + 112y = 168---------------(1)

First we have to find the gcd of 70 and 112.

112 = 70×1 + 42

70 = 42×1 +28

42 = 28×1 + 14

28 =14×2 + 0

∴gcd (70, 112) = 14

Therefore, equation (1) has a solution.

Dividing Equation(1) by 14 we get

5x + 8y = 12

We see that x = -4, y =4 satisfy the above equation. Its general solution is given

x₁=x₀-$\frac{112}{14}t$=(-4-8t)= -4(1+4t)

y₁=y₀-$\frac{70}{14}t$= 4+5t