Sure, let's solve this step by step.
Given the system of equations:
[tex]\[ 2M + 3L = 26 \][/tex]
[tex]\[ M + L = X \][/tex]
We know that [tex]\(M\)[/tex] represents the number of medium cups and [tex]\(L\)[/tex] represents the number of large cups.
First, we need to find suitable integer values for [tex]\(M\)[/tex] and [tex]\(L\)[/tex] that satisfy the first equation:
[tex]\[ 2M + 3L = 26 \][/tex]
By examining possible values, we eventually find that when [tex]\(M = 1\)[/tex] and [tex]\(L = 8\)[/tex], the equation balances out:
[tex]\[ 2(1) + 3(8) = 26 \][/tex]
[tex]\[ 2 + 24 = 26 \][/tex]
[tex]\[ 26 = 26 \][/tex]
Thus, the values that satisfy the equation are [tex]\(M = 1\)[/tex] and [tex]\(L = 8\)[/tex].
Now, substituting these values into the second equation:
[tex]\[ M + L = X \][/tex]
[tex]\[ 1 + 8 = 9 \][/tex]
So, [tex]\(M + L = 9\)[/tex].
In conclusion, she used:
- 1 medium cup ([tex]\(M = 1\)[/tex])
- 8 large cups ([tex]\(L = 8\)[/tex])
Therefore, the total number of cups is 9.
The completed equation is:
[tex]\[ M + L = 9 \][/tex]
