Question

Instructions: Determine the solution to the real world system by graphing.Eugene and Shanice each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Grass sod costs dollars and geraniums cost dollars. Eugene spent $36 on 9 ft² of grass sod and 2 geraniums. Shanice spent $63 on 9 ft² of grass sod and 5 geraniums. What is the solution to the system of equations? What is the cost of one ft² of grass sod and the cost of one geranium?

Answer 1

Given information:

Grass cost x dollars

Geraniums cost y dollars

Equation 1:

Eugene spent $36 on 9 ft^2 of grass sod and 2 geraniums:

$9x+2y=36$

Equation 2:

Shanice spent $63 on 9ft^2 of grass sod and 5 geraniums:

$9x+5y=63$

Graph:

Find two points in each line to graph it.

First equation:

$\begin{gathered} 9x+2y=36 \\ \\ When\text{ x=2, find y:} \\ 9(2)+2y=36 \\ 18+2y=36 \\ 2y=36-18 \\ 2y=18 \\ y=\frac{18}{2} \\ y=9 \\ \\ Point:(2,9) \\ \\ When\text{ y=0, find x:} \\ 9x+2(0)=36 \\ 9x=36 \\ x=\frac{36}{9} \\ x=4 \\ \\ Point:(4,0) \end{gathered}$

Second equation:

$\begin{gathered} 9x+5y=63 \\ \\ When\text{ x=2, find y:} \\ 9(2)+5y=63 \\ 18+5y=63 \\ 5y=63-18 \\ 5y=45 \\ y=\frac{45}{5} \\ y=9 \\ \\ Point:(2,9) \\ \\ When\text{ y=0, find x:} \\ 9x+5(0)=63 \\ 9x=63 \\ x=\frac{63}{9} \\ x=7 \\ \\ Point:(7,0) \end{gathered}$

Use the points to graph the system of equations:

Solution point: (2,9)ft^2 of grass sod (x): $2Geranium (y): $9