the complete question is
The scouts sold small and large boxes of cookies as a fund raiser. One scout sold 7 small boxes and 12 large boxes for $54.00. Another scout sold 5 small boxes and 10 large boxes for $60.00. The scout leader wrote a system of equations to represent the their sales.
Which constants can each equation be multiplied by so that one variable is eliminated when the equations are added?
let
x------> cost small boxes
y-----> cost large boxes
we know that
7x+12y=54------> equation 1
5x+10y=60------> equation 2
step 1
multiply equation 1 by (-5/7)
so
(-5/7)*{7x+12y=54}----> -5x-(60/7)y=-270/7
-5x-(60/7)y=-270/7
5x+10y=60
-----------------
by adding the equations the variable x is eliminated
step 2
multiply equation 1 by (-10/12----> -5/6)
so
(-5/6)*{7x+12y=54}---->(-35/6)x-10y=-45
(-35/6)x-10y=-45
5x+10y=60
-----------------
by adding the equations the variable y is eliminated
step 3
multiply equation 2 by (-7/5)
so
(-7/5)*{5x+10y=60}------> -7x-(70/5)y=-84
-7x-(70/5)y=-84
7x+12y=54
---------------------
by adding the equations the variable x is eliminated
step 4
multiply equation 2 by (-12/10-----> -6/5)
so
(-6/5)*{5x+10y=60}------> -6x-12y=-72
-6x-12y=-72
7x+12y=54
---------------------
by adding the equations the variable y is eliminated