Question

Three times a number plus three times a second number is negative twelve. Five times the first number plus twice the second is four

Answer 1

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 :

${:\implies \quad \begin{cases}\sf 3x+3y=-12\\ \\ \sf 5x+2y=4\end{cases}}$

Now, rewrite the second equation as ;

${:\implies \quad \sf 3(x+y)=-12}$

Divide both sides by 3 ;

${:\implies \quad \sf x+y=-4\quad ---(i)}$

Now, consider the second equation of the above cases

${:\implies \quad \sf 5x+2y=4\quad ---(ii)}$

Now, multiply (i) by 2 on both sides :

${:\implies \quad \sf 2x+2y=-8\quad ---(iii)}$

Now, subtracting (ii) from (iii) will give us :

${:\implies \quad \sf 2x+2y-(5x+2y)=-8-4}$

${:\implies \quad \sf 2x+2y-5x-2y=-12}$

${:\implies \quad \sf -3x=-12}$

${:\implies \quad \boxed{\bf{x=4}}}$

Now, putting x = 4 in (i), will give y + 4 = -4, then solving for y will yield ${\boxed{\bf{y=-8}}}$

Hence, we can conclude that :

${\quad \qquad \longrightarrow \begin{cases}\bf x=4\\ \\ \bf y=-8\end{cases}}$