Question

At a local garden shop, the price of plants includes
sales tax. The cost of 4 large plants and 8 medium
plants is $40. The cost of S large plants and 2 medium plants is$28. If / is the cost of a large
plant and m is the cost of a medium plant, write a
system of equations that models this situation.
Could the cost of one large plant be $5.50 and the cost of one medium plant be$2.25? Justify your
answer. Determine algebraically both the cost of a
large plant and the cost of a medium plant.

1. 4L + 8 m = $40 5L + 2m =$28
Stepbystep explanation:
L = cost of a large plant
m = cost of a medium plant 4L + 8 m = $40 5L + 2m =$28

2. Equation (1) and equation (2) represent the system of equations, the cost of the large plant is $4.5, and the cost of the medium plant is$2.75

### What is a linear equation?

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
We have:
l is the cost of a large plant and m is the cost of a medium plant.
The cost of 4 large plants and 8 medium plants is $40. For the above scenario, the linear expression can be written as in two variables: 4l + 8m = 40 …(1) The cost of 5 large plants and 2 medium plants is$28 for this scenario, the linear expression can be written as in two variables:
5l + 2m = 28 …(2)
Multiplying the above equation with 4 on both sides
20l + 8m = 112 …(3)
Subtracting equation (1) from equation (2), we get:
20l – 4l = 112 – 40
16l = 72
l = $4.5 Put this value in the equation (1), we get: 4(4.5) +8m = 40 18 +8m = 40 m =$2.75
Thus, the equation (1) and equation (2) represent the system of equations, the cost of the large plant is $4.5, and the cost of the medium plant is$2.