Question

Solve the following equations graphically :
x + 4y + 9 = 0
3y = 5x - 1

Answer 1

x + 4y + 9 = 0
3y = 5x - 1
x + 4y + 9 _______(1)
3y = 5x - 1_______(2)
Now, x + 4y = -9
⇒ x = -9 - 4y
Corresponding values of x and y can be tabulated as :

x	4	-1	-5
y	-3	-2	-1

Plotting points (4, -3), (-1, -2) and (-5, -1) and joining them, we geta line l₁  which is the graph of equation (!).
Again, 3y = 5 x -1

⇒ y = `(5x - 1)/(3)`
Corresponding values of x and y can be tabulated as :

x	-4	-1	5
y	-7	-2	8

Plotting points (-4, -7), (-1, -2), (5, 8) and joining them we get a line l₂ which is the graph of equation (2).

The two line l₁ and l₂ intersect at a unique point (-1, -2). Thus, x = -1 and y = -2 is the unique solution of the given equations.