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.
x | 0 | 3 |
y | 6 | 0 |
Points | B | A |
Table for equation 2x – y + 2 = 0, for x = 0, y = 2, for y = 0,x = - 1
x | 0 | - 1 |
y | 2 | 0 |
Points | D | C |
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.