Answer :
Let x be the greater integer
Let y be the smaller integer
their sum is one hundred and seventy one:
[tex]x+y=171[/tex]their difference is twenty-five:
[tex]x-y=25[/tex]Use the next system of equations:
[tex]\begin{gathered} x+y=171 \\ x-y=25 \end{gathered}[/tex]1. Solve y in the second equation:
[tex]\begin{gathered} x-y=25 \\ -y=25-x \\ y=-25+x \end{gathered}[/tex]2. Substitute the y in the first equation by th value you get in step 1:
[tex]x+(-25+x)=171[/tex]3. Solve x:
[tex]\begin{gathered} x-25+x=171 \\ 2x-25=171 \\ 2x=171+25 \\ 2x=196 \\ x=\frac{196}{2} \\ \\ x=98 \end{gathered}[/tex]