By using the elimination method, the first number is 3 and the second number is 0.
- Let the first number be a.
- Let the second number be b.
Translating the word problem into an algebraic expression, we have;
Four times one number minus three times another number is 12:
[tex]4a -3b=12[/tex] ...equation 1.
Two times the first number added to three times to the second number is 6:
[tex]2a+3b=6[/tex] ...equation 2.
Applying the elimination method, we have:
[tex](4a+2a)+(-3b+3b)=12+6\\\\6a=18\\\\a=\frac{18}{6}[/tex]
a = 3
For the value of the second number:
[tex]2a+3b=6\\\\2(3)+3b=6\\\\6+3b=6\\\\3b=0\\\\b=0[/tex]
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