Solve the pair of linear equations graphically 𝑥 + 3𝑦 = 6 and 2𝑥 − 3𝑦 = 12

Also shade the region bounded by the line 2𝑥 − 3𝑦 = 12 and both the coordinates. 

: Given equations are

 𝑥 + 3𝑦 = 6 …(𝑖) 

2𝑥 − 3𝑦 = 12 …(𝑖𝑖)

 From (𝑖), 𝑥 = 6 − 3𝑦

From (𝑖𝑖), 𝑥 = $From (𝑖𝑖), 𝑥 = \frac{12+3y}{2}$

By plotting the points in the graph, we get

Both lines intersect at (6, 0)