Question 1047160
{{{19}}}= number of 1-point baskets/shots
{{{x}}}= number of 2-point baskets/shots
{{{y}}}= number of 3-point baskets/shots
{{{19+2x+3y}}}= total number of points scored.
"Team scored 78" translates as
{{{19+2x+3y=78}}}
We translate "the remaining 27 were two points or three point shots" as
{{{x+y=27}}} .
We have a system of two equations: {{{system(19+2x+3y=78,x+y=27)}}} .
You could easily solve {{{x+y=27}}} for {{{x}}} :
{{{x+y=27}}} ---> {{{x=27-y}}} ,
and then substitute {{{27-y}}} for {{{x}}} in the other equation to get
{{{19+2(27-y)+3y=78}}}
{{{19+54-2y+3y=78}}}
{{{73+y=78}}}
{{{y=78-73}}}
{{{highlight(y=5)}}} .
Then, substituting {{{5}}} for {{{y}}} in {{{x=27-y}}} , you get
{{{x=27-5}}}
{{{highlight(x=22)}}} .
 
NOTE:
If you have not studied systems of equations,
you could start with
{{{19}}}= number of 1-point baskets/shots
{{{y}}}= number of 3-point baskets/shots,
and since "the remaining 27 were two points or three point shots"
{{{27-y}}}= number of 3-point baskets/shots
"Team scored 78" then translates as
{{{19+2(27-y)+3y=78}}} ,
and that equation can be solved for {{{y}}} as shown above.
 
OTHER WAYS: There are other ways to solve the system of equations,
but the result is the same:
there were {{{highlight(5)}}} 3-point shots,
and {{{highlight(22)}}} 2-point shots.