Question

Solve the following equations graphically :
2x + 4y = 7
3x + 8y = 10

Answer 1

2x + 4y = 7
3x + 8y = 10
2x + 4y = 7  _________(1)
3x + 8y = 10 ________(2)
Now, 2x + 4y = 7
⇒ 4y = 7 - 2x

⇒ y = `(7 - 2x)/(4)`
Corresponding values of x and y can be tabulated as :

x	2	3	4
y	0.75	0.25	-0.25

Plotting points (2, 0.75), (3, 0.25), (3, 0.25), (4, -0.25) and joining them, we get a line l₁ which is the graph of equation (1).
Again, 3x + 8y = 10

⇒ x = `(10 - 8y)/(3)`
Corresponding values of x and y can be tabulated as :

x	6	-2	0
y	-1	2	1.25

Plotting points (6, 1), (2, 2), (0, 1.25) and joining them, we get a line l₂ which is the graph of equation (2).

The two lines l₁ and l₂ intersect at the point (4, -0.25), i.e., `(4,-1/4)`.

Hence x = 4 and y = `(-1)/(4)` is the unique solution of the given equations.