If one is in ratio the other one is zero

If one is in ratio the other one is zero.

Problem: Find the value of x and y.

2x + 4y = 8          (eq.1)

6x + 8y = 24        (eq.2)

Notice 2x & 6x and also 8 & 24, they are in ratio, therefore y = 0 .

2x:6x and 8:24 = 1:3 ratio

Solution:

y = 0

2x = 8

x = 4

Press the buzzer or raise your hand.

"Sir! x = 4 and y = 0 !"

Here is why or how:

Multiplying equation 1 by 3.

(2x + 4y = 8) x 3

6x + 12y = 24       (eq.3)

Then, subtract equation 2 from equation 3.

    6x + 12y = 24    (eq.3)

(-) 6x +   8y = 24    (eq.2)

=  0   +   4y = 0

                y = 0

When one is zero, you can solve for the other one with just one equation.

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