I NEED HELP WITH FINITE

Question

A player scored 93 points in a single professional basketball game. He made a total of 59

​baskets, consisting of field goals​ (worth two​ points) and foul shots​ (worth one​ point). Find the number of field goals and the number of foul shots that the player made.

Answer 1

Let "x" be the number of field goals (2-pointers) made and let "y" be the number of foul shot (1-pointers) made.

Since there were 59 baskets made, then x + y = 59. Since there were 93 points made, then 2x + 1y = 93

Solve the two equations using a variety of means. An easy way is the make the first equation say y = 59 - x then plug in "59 - x" into the 2nd equation in place of "y" (since "y" and "59 - x" are the same)

2x + 1y = 93

2x + y = 93

2x + (59 - x) = 93

2x - x + 59 = 93

x + 59 = 93

x = 93 - 59

x = 34

Since we already determined that y = 59 - x then y = 59 - 34 or y = 25

So the player scored 34 field goals and 25 foul shots

Answer 2

Let x=number of field goal points made

y=number of foul shots made

x+y=59

2x+y=93

y=59-x

2x+(59-x)=93

x=34

y=59-34

y=25