A system of equations comprising of '26t + 38d = 180' for the front yard and '18t + 32d = 136' for the backyard is used to determine the cost of tulip and daffodil bulbs, where t is the price per tulip bulb and d is the price per daffodil bulb.
To determine the cost of each type of flower bulb (tulips and daffodils) using the information provided, we set up a system of linear equations.
Let t be the price of one tulip bulb and d be the price of one daffodil bulb. From the purchase for the front yard, we have the equation 26t + 38d = 180 since there were 26 tulip bulbs and 38 daffodil bulbs bought for a total of $180.
For the backyard, we have the equation 18t + 32d = 136 because the student bought 18 tulip bulbs and 32 daffodil bulbs for $136.
The system of equations to find out the cost of each bulb is:
26t + 38d = 180
18t + 32d = 136
By solving this system, we can find the values of t and d, which are the prices per tulip bulb and per daffodil bulb, respectively.