Graphically, solve the following pair of equations

2x + y = 6 and 2x – y + 2 = 0

Find the ratio of the areas of the two triangles formed by the lines representing these equations with the X - axis and the lines with the Y - axis.

Given equations are 2x + y = 6 and 2x – y + 2 = 0

Table for equation 2x + y - 6 = 0, for x = 0, y = 6, for y = 0, x = 3.

Table for equation 2x – y + 2 = 0, for x = 0, y = 2, for y = 0,x = - 1

Let A₁ and A₂ represent the areas of and & respectively where E is the intersection of lines.

Now, Area of triangle formed with x -axis =

=

And Area of triangle formed with y - axis =

Hence, the pair of equations intersect graphically at point E(1,4)

i.e., x = 1 and y = 4.