Question

Solve the following equations graphically :
2x - y = 9
5x + 2y = 27

Answer 1

2x - y = 9
5x + 2y = 27
2x - y = 9 _________(1)
5x + 2y = 27 ________(2)
Now, 2x - y = 9
⇒ y = 2x - 9
Corresponding values of x and y can be tabulated as :

x	2	3	4
y	-5	-3	-1

Plotting points (2, -5), (3, -3), (4, -1) and joining them, we get a line l, which is the graph pf equation (1).
Again, 5x + 2y = 27

⇒ y = `(27 - 5x)/(2)`
Corresponding values of x and y can be tabulated as :

x	5	4	3
y	1	3.5	6

Plotting points (5, 1), (4, 3.5), (3, 6) and joining them, we get a line l₂ which is the graph of equation (2).

The two lines l₁ and l₂ intersect at a unique point (5, 1).
Thus, x = 5 and y = 1 is the unique solution of the given equations.