To solve this problem, we need to determine how many ounces of jam each large jar and small jar can hold, given two conditions.

Step 1: Define Variables

Let:

• $x$ = the number of ounces a large jar can hold
• $y$ = the number of ounces a small jar can hold

Step 2: Form the System of Equations

From the problem, we know:

1. One large jar and two small jars together can hold 8 ounces of jam: $x + 2y = 8$
2. One large jar minus one small jar can hold 2 ounces of jam: $x - y = 2$

Now, we have the following system of equations:

1. $x + 2y = 8$
2. $x - y = 2$

Step 3: Matrix Representation

Coefficient Matrix

The coefficient matrix is made up of the coefficients of $x$ and $y$ in the system of equations. From the equations, the coefficient matrix is:

1 & 2 \\ 1 & -1 \end{pmatrix}$$ #### Variable Matrix The variable matrix contains the unknowns $$x$$ and $$y$$: $$\begin{pmatrix} x \\ y \end{pmatrix}$$ #### Solution Matrix The solution matrix contains the constants on the right-hand side of the equations: $$\begin{pmatrix} 8 \\ 2 \end{pmatrix}$$ ### Step 4: Complete Matrix Equation The matrix equation combining the coefficient, variable, and solution matrices is: $$\begin{pmatrix} 1 & 2 \\ 1 & -1 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 8 \\ 2 \end{pmatrix}$$ This is the matrix setup to solve for $$x$$ (the capacity of the large jar) and $$y$$ (the capacity of the small jar). Would you like me to solve this system of equations for the values of $$x$$ and $$y$$? --- Here are 5 related questions: 1. How can this system be solved using the elimination method? 2. What happens if we increase the number of small jars in the first equation? 3. Can this system be solved using the substitution method? 4. What is the geometric interpretation of this system of equations? 5. How can we use matrix inversion to solve for $$x$$ and $$y$$? **Tip:** For systems of linear equations, matrix methods like Gaussian elimination or finding the inverse are powerful tools when dealing with multiple variables.