Hi there! Let me know if you have questions about my answer:
One shrub is $11.
One daylily is $4.
Step-by-step explanation:
To find the cost of each item, write a system of equations, one equation for what each person bought, and solve for each variable.
<u>Define your variables.</u>
let 'd' be the cost of one daylily
let 'r' be the cost of one shrub
<u>Create a system using the variables and information from the question.</u>
Write an equation for what Arjun bought:
5d + 7r = 97            5 daylilies, 7 shrubs, totaling $97
Write an equation for what Jessica bought:
2d + 11r = 129          2 daylilies, 11 shrubs, totaling $129
<u>Solve the system.</u>
I will solve the system algebraically, using the substitution method. Isolate one variable in one of the equations. 
I will isolate 'd' in Jessica's equation:
 Start with Jessica's equation
              Start with Jessica's equation
 Divide everything in the equation by 2
                  Divide everything in the equation by 2
 Simplify
                 Simplify
 Isolate 'd' by subtracting
                 Isolate 'd' by subtracting  from both sides.
 from both sides.
Now you have an expression for 'd'.
Substitute Arjun's equation with the expression for 'd'. Solve for 'r' to find the cost of one shrub.
 Start with Arjun's equation
                      Start with Arjun's equation
 Substitute 'd' for
       Substitute 'd' for  
 Distribute the 5
      Distribute the 5
 Simplify the numerators
            Simplify the numerators
 Change 7r to a fraction over 2
          Change 7r to a fraction over 2
 Combine like terms, the terms with 'r'
                    Combine like terms, the terms with 'r'
 Simplify
                       Simplify
 Multiply both sides by 2
                 Multiply both sides by 2
 Subtract 645 from both sides
              Subtract 645 from both sides
 Divide both sides by –41
                     Divide both sides by –41
 Solved for cost of one shrub
                                Solved for cost of one shrub
Substitute 'r' for 11 using either Arjun's or Jessica's equation. Then, isolate 'd' to solve for the cost of one daylily.
I will use Arjun's equation.
 Start with Arjun's equation
                   Start with Arjun's equation
 Substitute 'r' for r = 11
              Substitute 'r' for r = 11
 Simplify. Subtract 77 from both sides.
                   Simplify. Subtract 77 from both sides.
 Divide both sides by 5.
                           Divide both sides by 5.
 Solved for the cost of one daylily
                              Solved for the cost of one daylily
I hope this helped! Check out a similar problem about solving systems here to learn more:
brainly.com/question/11103098