Solve the pair of linear equations `3x-y=3 and 7x+2y=20.`

Answer

To solve the pair of linear equations \(3x - y = 3\) and \(7x + 2y = 20\), we can use the method of elimination. Here’s a step-by-step solution:

### Step 1: Write the equations
We have the following equations:
1. \(3x - y = 3\) (Equation 1)
2. \(7x + 2y = 20\) (Equation 2)

### Step 2: Make the coefficients of \(y\) the same
To eliminate \(y\), we can multiply Equation 1 by 2. This gives us:
\[ 2(3x - y) = 2(3) \\ 6x - 2y = 6 \quad \text{(Equation 3)} \]

### Step 3: Write the modified equations
Now we have:
1. \(6x - 2y = 6\) (Equation 3)
2. \(7x + 2y = 20\) (Equation 2)

### Step 4: Add the two equations
Now, we will add Equation 3 and Equation 2:
\[ (6x - 2y) + (7x + 2y) = 6 + 20 \\ 6x + 7x - 2y + 2y = 26 \\ 13x = 26 \]

### Step 5: Solve for \(x\)
Now, divide both sides by 13:
\[ x = \frac{26}{13} = 2 \]

### Step 6: Substitute \(x\) back into one of the original equations
Now that we have \(x\), we can substitute it back into Equation 1 to find \(y\):
\[ 3(2) - y = 3 \\ 6 - y = 3 \]

### Step 7: Solve for \(y\)
Rearranging gives:
\[ -y = 3 - 6 \\ -y = -3 \\ y = 3 \]

### Final Solution
Thus, the solution to the pair of linear equations is:
\[ x = 2 \quad \text{and} \quad y = 3 \]