Interpreting the situation, we have that:
a) The system of equations is:
[tex]y = 2x - 7[/tex]
[tex]y = 6 + x[/tex]
b) Solving the above system, it is found that Jacob scored 13 and Paul scored 19.
Item a:
In our system, we have that:
- Jacob's score is of x.
- Paul's score is of y.
Jacob said that Paul's score would be twice his own score if he earned 7 more points, which means that:
[tex]y + 7 = 2x[/tex]
[tex]y = 2x - 7[/tex]
Paul responded to Jacob by telling him his score was only 6 points higher then Jacob's, which means that:
[tex]y = 6 + x[/tex]
Item b:
Equaling both equations:
[tex]2x - 7 = 6 + x[/tex]
[tex]x = 13[/tex]
[tex]y = 6 + x = 6 + 13 = 19[/tex]
Jacob scored 13 and Paul scored 19.
A similar problem is given at https://brainly.com/question/24104709
