Use the method of plugging In to solve the following problem.
Which one of the following is the solution of the system of equations given ?
`x + 2y = 7`
`x + y = 4`

Options

A. `x = 3, y = 2`
B. `x = 2, y = 3`
C. `x = 1, y = 3`
D. `x = 3, y =1`

Answer

To solve the system of equations using the method of plugging in, we have the following equations:

1. \( x + 2y = 7 \) (Equation 1)
2. \( x + y = 4 \) (Equation 2)

We will check each option given to see which one satisfies both equations.

### Step 1: Check Option A
Let’s assume \( x = 3 \) and \( y = 2 \).

**Substituting into Equation 1:**
\[ x + 2y = 7 \implies 3 + 2(2) = 3 + 4 = 7 \]
This satisfies Equation 1.

**Substituting into Equation 2:**
\[ x + y = 4 \implies 3 + 2 = 5 \]
This does not satisfy Equation 2. Therefore, Option A is not a solution.

### Step 2: Check Option B
Let’s assume \( x = 2 \) and \( y = 3 \).

**Substituting into Equation 1:**
\[ x + 2y = 7 \implies 2 + 2(3) = 2 + 6 = 8 \]
This does not satisfy Equation 1.

**Substituting into Equation 2:**
\[ x + y = 4 \implies 2 + 3 = 5 \]
This does not satisfy Equation 2 either. Therefore, Option B is not a solution.

### Step 3: Check Option C
Let’s assume \( x = 1 \) and \( y = 3 \).

**Substituting into Equation 1:**
\[ x + 2y = 7 \implies 1 + 2(3) = 1 + 6 = 7 \]
This satisfies Equation 1.

**Substituting into Equation 2:**
\[ x + y = 4 \implies 1 + 3 = 4 \]
This satisfies Equation 2 as well. Therefore, Option C is a solution.

### Conclusion
The solution to the system of equations is given by Option C: \( (x, y) = (1, 3) \).

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