Two unknown numbers

One number is two less than a second number. Twice the second number is 14 lower than five times the first. Find the two numbers.

Correct answer:

a =  6
b =  8

Step-by-step explanation:


a = b-2
2b = 5a - 14

a = b-2
2·b = 5·a - 14

a-b = -2
5a-2b = 14

Pivot: Row 1 ↔ Row 2
5a-2b = 14
a-b = -2

Row 2 - 1/5 · Row 1 → Row 2
5a-2b = 14
-0.6b = -4.8


b = -4.8/-0.6 = 8
a = 14+2b/5 = 14+2 · 8/5 = 6

a = 6
b = 8

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