Problem Breakdown:

The given problem consists of two sets of equations involving sums of variables $a$, $b$, $c$, and $d$:

1. The top set shows two squares, one with $a + b$, and the other with $c + b$. Together, these sums equal 15.
2. The bottom set shows a similar layout with values (c+d =15 Let me break down and solve the problem in your image.

Step 1: Analyze the Problem

The grid involves four variables $a$, $b$, $c$, and $d$. The equations derived from the grid are:

1. $a + b = 15$
2. $c + d = 15$
3. $a + c = 12$
4. $b + d = 2$

We need to:

1. Write the equations in terms of $a$, $b$, $c$, and $d$.
2. Solve for the values of $a$, $b$, $c$, and $d$.

Step 2: Write the System of Equations

From the given sums:

• $a + b = 15$ $\Rightarrow$ Equation 1
• $c + d = 15$ $\Rightarrow$ Equation 2
• $a + c = 12$ $\Rightarrow$ Equation 3
• $b + d = 2$ $\Rightarrow$ Equation 4

Step 3: Solve the System of Equations

Using substitution:

• From Equation 1: $b = 15 - a$
• From Equation 2: $d = 15 - c$

Substitute $b$ and $d$ into Equation 4: $(15 - a) + (15 - c) = 2$ Simplify: $30 - a - c = 2 \Rightarrow a + c = 28$

Now we have two equations for $a + c$:

1. $a + c = 12$ (from Equation 3)
2. $a + c = 28$ (contradiction suggests a misrepresentation).

Let us revisit and systematically solve the equations based on the relationships given in the image.

The system of equations extracted from the image is as follows:

1. $a + b = 15$ (Equation 1)
2. $c + d = 15$ (Equation 2)
3. $a + c = 12$ (Equation 3)
4. $b + d = 2$ (Equation 4)

Solve the Equations Step by Step:

• From Equation 1: $b = 15 - a$
• From Equation 2: $d = 15 - c$

Substitute $b = 15 - a$ and $d = 15 - c$ into Equation 4: $(15 - a) + (15 - c) = 2$ Simplify: $30 - a - c = 2$ $a + c = 28$

Now we have two equations for $a + c$:

1. $a + c = 12$ (Equation 3)
2. $a + c = 28$ (from solving Equation 4).

Clearly, the values of $a$, $b$, $c$, and $d$ need reconciliation. Can you confirm the exact alignment of values in your query? If there’s a mismatch, I can resolve it further!