Solve the following pair of linear equations by substitution method:
x+2y=2
x-3y=7

Options

A. (2.1)
B. (1,0)
C. (4,-1)
D. (0,4)

Answer

To solve the given pair of linear equations using the substitution method, we will follow these steps:

1. **Write down the equations:**
\[ \text{Equation 1: } x + 2y = 2 \quad (1) \]
\[ \text{Equation 2: } x - 3y = 7 \quad (2) \]

2. **Solve one of the equations for one variable:**
Let's solve Equation (1) for \(x\):
\[ x = 2 - 2y \quad (3) \]

3. **Substitute the expression for \(x\) from Equation (3) into Equation (2):**
Replace \(x\) in Equation (2):
\[ (2 - 2y) - 3y = 7 \]

4. **Simplify the equation:**
Combine like terms:
\[ 2 - 2y - 3y = 7 \]
\[ 2 - 5y = 7 \]

5. **Isolate \(y\):**
Subtract 2 from both sides:
\[ -5y = 7 - 2 \]
\[ -5y = 5 \]
Now divide both sides by -5:
\[ y = -1 \quad (4) \]

6. **Substitute the value of \(y\) back into Equation (3) to find \(x\):**
Substitute \(y = -1\) into Equation (3):
\[ x = 2 - 2(-1) \]
\[ x = 2 + 2 \]
\[ x = 4 \quad (5) \]

7. **Write the solution as an ordered pair:**
The solution to the system of equations is:
\[ (x, y) = (4, -1) \]