The solution of equations `3x+4y=10 and x-y=1` is :

Options

A. `x=2, y=3`
B. `x=-2, y=1`
C. `x=2, y=1`
D. None of these

Answer

To solve the equations \(3x + 4y = 10\) and \(x - y = 1\), we will follow these steps:

### Step 1: Write down the equations
We have the following two equations:
1. \(3x + 4y = 10\) (Equation 1)
2. \(x - y = 1\) (Equation 2)

### Step 2: Express one variable in terms of the other
From Equation 2, we can express \(y\) in terms of \(x\):
\[ x - y = 1 \implies y = x - 1 \]

### Step 3: Substitute the expression for \(y\) into Equation 1
Now, we will substitute \(y = x - 1\) into Equation 1:
\[ 3x + 4(x - 1) = 10 \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ 3x + 4x - 4 = 10 \]
Combine like terms:
\[ 7x - 4 = 10 \]

### Step 5: Solve for \(x\)
Add 4 to both sides:
\[ 7x = 10 + 4 \]
\[ 7x = 14 \]
Now, divide by 7:
\[ x = \frac{14}{7} = 2 \]

### Step 6: Substitute \(x\) back to find \(y\)
Now that we have \(x\), we can find \(y\) using the expression we found in Step 2:
\[ y = x - 1 = 2 - 1 = 1 \]

### Final Solution
The solution to the equations is:
\[ x = 2, \quad y = 1 \]