Question

Solve the following pair of linear equations by graphical method : \(2x + y = 9\) and \(x - 2y = 2\).

Answer 1

Graphical Solution of a Pair of Linear Equations

Given Equations:

• Equation 1: \(2x + y = 9\)
• Equation 2: \(x - 2y = 2\)

Rewriting in Slope-Intercept Form

Equation 1: \( y = 9 - 2x \)
Equation 2: \( y = \frac{x - 2}{2} \)

Points for Graphing

Equation 1: \( y = 9 - 2x \)

• When \( x = 0 \), \( y = 9 \) → (0, 9)
• When \( x = 2 \), \( y = 5 \) → (2, 5)
• When \( x = 4 \), \( y = 1 \) → (4, 1)

Equation 2: \( y = \frac{x - 2}{2} \)

• When \( x = 0 \), \( y = -1 \) → (0, -1)
• When \( x = 2 \), \( y = 0 \) → (2, 0)
• When \( x = 4 \), \( y = 1 \) → (4, 1)

Graphical Intersection

Plotting both lines, we observe that they intersect at the point: \[ (4, 1) \] This is the solution to the system of equations.

Verification

Substitute \( x = 4 \), \( y = 1 \) into both equations:

Equation 1:

\[ 2x + y = 2(4) + 1 = 8 + 1 = 9 \quad \text{✔ True} \]

Equation 2:

\[ x - 2y = 4 - 2(1) = 4 - 2 = 2 \quad \text{✔ True} \]

✅ Final Answer:

The solution is: \[ \boxed{x = 4,\ y = 1} \]