Question

A credit card company offers a cash back program on transactions. For every transaction over​ $100 the customer gets ​$3 back. For every transaction​ $100 or​ less, the customer gets​ $1 back. The customer made 25 transactions in all and the total number of dollars given back was ​$29. Write and solve a system of equations to find the number of transactions of each type.

Answer 1

The first equation is $3 times 9 = $27 the next equation iis $1 times 2 = $1
So you do 9 transactions over $100 and 2 transactions of $100 or lower. 

Answer 2

x=over 100
y=100 or less

x+y=25
3x+1y=29

sole
mltiply first equation by -1 and add to other equation

-1x-1y=-25
3x+1y=29 +
2x+0y=4

2x=4
divide by 2
x=2

sub back
x+y=25
2+y=25
minus 2
y=23


there were 2 transactions more than 100
there were 23 transactions 100 or less