Step 1. First, let's define the variable we are going to use:

Step 2. Find the first equation from the information about James.
James spends $77 on 7 daylilies and 8 shrubs, this is described in the following equation:

Step 3. To find the second equation we use the information about Liz.
Liz spends $140 on 14 daylilies and 14 shrubs. The equation describing this is:

Since all of the numbers involved in this equation are multiples of 14, we can divide the whole equation by 14 to simplify it:

Step 4. Define the system of equations.
From step 2 and step 3 we have our two equations:

Step 5. The method we will use to solve this system of equations is the substitution method. To use this method, we solve one of the equations for 1 variable. In our case, we solve the second equation for d:

And the second step of the substitution method is to substitute that value into the first equation:

Step 6. Solve the previous equation for s.

using the distributive property to multiply 7 by 10 and 7 by -s:

Combining like terms:

Subtracting 70 to both sides of the equation:

The cost of one shrub is $7.
Step 7. Now that we know the value of s, we can find the value of d using the equation we had previously solved for d in step 5:

Substituting s=7:

The cost of one daylily is $3.
Answer:
The cost of one shrub is $7 and the cost of one daylily is $3.