x - Jack's age
y - Susan's age
Jack is 27 years older than Susan.
[tex]x=y+27[/tex]
In 5 years he will be 4 times as old as she is.
[tex]x+5=4(y+5)[/tex]
The system of equations:
[tex]x=y+27 \\ x+5=4(y+5) \\ \\ \hbox{substitute y+27 for x in the 2nd equation:} \\ y+27+5=4(y+5) \\ y+32=4y+20 \\ y-4y=20-32 \\ -3y=-12 \\ y=\frac{-12}{-3} \\ y=4 \\ \\ x=y+27=4+27=31[/tex]
Jack is 31 years old and Susan is 4 years old.
