Respuesta :
Answer:
Step-by-step explanation:
Let [tex] x[/tex] be the greater number and [tex] y [/tex] be the smaller number. We know that their difference is 15, so we have
[tex] x-y=15 [/tex]
Then, we have the following information: if we add twice the greater (2x) and 8 (2x+8), the result is 3 times the lesser (3y) minus four (3y-4). So, we have
[tex] 2x+8 = 3y-4 \iff 2x-3y = -12 [/tex]
So, we have the follwing system:
[tex] \begin{cases} x-y=15\\2x-3y = -12\end{cases} [/tex]
From the first equation, we can derive [tex] x = y+15 [/tex], and substitute this expression in the second equation to get
[tex] 2(y+15)-3y = -12 \iff 2y + 30 -3y = -12 \iff -y = -42 \iff y = 42 [/tex]
Substitute this value for y in the first equation to get
[tex] x-42=15 \iff x=15+42 \iff x = 57 [/tex]
