Question

find two different solution of the equation 2x + 3y =12​

Answer 1

Given :-

• Equation of line is 2x + 3y = 12

To Find :-

• Two different solutions

Solution :-

Given equation of line is

$\rm :\longmapsto\:2x + 3y = 12 - - - (1)$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:2 \times 0 + 3y = 12$

$\rm :\longmapsto\:0 + 3y = 12$

$\rm :\longmapsto\:3y = 12$

$\bf\implies \:y = 4$

Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:2x + 3 \times 0 = 12$

$\rm :\longmapsto\:2x + 0 = 12$

$\rm :\longmapsto\:2x = 12$

$\bf\implies \:x = 6$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 4 \\ \\ \sf 6 & \sf 0 \end{array}} \\ \end{gathered}$

Basic Concept :-

Let us consider the general equation of line ax + by + c = 0,

• then any pair of values of x and y, i.e, (x, y) satisfies the given equation is called Solution of line.

The linear equation ax + by + c = 0 have infinitely many solutions.

Through a point, infinitely many lines can passes.