Respuesta :
Consider the numbers as, if we assume our first number to be x and second number being y, then from the given information we will be having the following equations :
[tex]{:\implies \quad \begin{cases}\sf 3x+3y=-12\\ \\ \sf 5x+2y=4\end{cases}}[/tex]
Now, rewrite the second equation as ;
[tex]{:\implies \quad \sf 3(x+y)=-12}[/tex]
Divide both sides by 3 ;
[tex]{:\implies \quad \sf x+y=-4\quad ---(i)}[/tex]
Now, consider the second equation of the above cases
[tex]{:\implies \quad \sf 5x+2y=4\quad ---(ii)}[/tex]
Now, multiply (i) by 2 on both sides :
[tex]{:\implies \quad \sf 2x+2y=-8\quad ---(iii)}[/tex]
Now, subtracting (ii) from (iii) will give us :
[tex]{:\implies \quad \sf 2x+2y-(5x+2y)=-8-4}[/tex]
[tex]{:\implies \quad \sf 2x+2y-5x-2y=-12}[/tex]
[tex]{:\implies \quad \sf -3x=-12}[/tex]
[tex]{:\implies \quad \boxed{\bf{x=4}}}[/tex]
Now, putting x = 4 in (i), will give y + 4 = -4, then solving for y will yield [tex]{\boxed{\bf{y=-8}}}[/tex]
Hence, we can conclude that :
[tex]{\quad \qquad \longrightarrow \begin{cases}\bf x=4\\ \\ \bf y=-8\end{cases}}[/tex]
