Respuesta :
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Represent the unknown numbers with variable x and y
[tex]\begin{gathered} \text{From statement 1} \\ x=y+6----\text{equation 1} \\ \text{This implies that x is the bigger number and y is the smaller number} \\ \text{From statement 2} \\ \text{ sum of twice the smaller num}ber=2y \\ \text{thr}ee\text{ times the larger number}=3x \\ \text{Result is -7, then,} \\ 3x+2y=-7-----\text{equation 2} \end{gathered}[/tex]STEP 2: Write out the derived equations
[tex]\begin{gathered} x=y+6---\text{equation 1} \\ 3x+2y=-7---\text{equation 2} \\ \text{making x the subject of equation 2} \\ 3x=-7-2y \\ \text{Divide both sides by 3} \\ \frac{3x}{3}=\frac{-7-2y}{3} \\ x=\frac{-7-2y}{3} \end{gathered}[/tex]STEP 3: Solve for x
[tex]\begin{gathered} x=y+6 \\ x-6=y \\ \text{substitute x-6 for y in equation 2} \\ 3x+2(x-6)=-7 \\ 3x+2x-12=-7 \\ 5x-12=-7 \\ \text{Add 12 to both sides} \\ 5x-12+12=-7+12 \\ 5x=5 \\ \text{Divide both sides} \\ \frac{5x}{5}=\frac{5}{5} \\ x=1 \end{gathered}[/tex]Hence, the equation in terms of x is:
[tex]\begin{gathered} x=y+6 \\ x=\frac{-7-2y}{3} \end{gathered}[/tex]And the value of x is 1
