Question

Solve the following system of equations graphically:
6x - 3y + 2 = 7x + 1
5x + 1 = 4x - y + 2
Also, find the area of the triangle formed by these lines and x-axis in each graph.

Answer 1

The given system of equations are
6x - 3y + 2 = 7x + 1 and 5x + 1 = 4x - y + 2
Now, 6x - 3y + 2
= 7x + 1     ....(1)
⇒ x = 1 - 3y
Corresponding values of x and y can be tabulated as :

x	1	-2	4
y	0	1	-1

Plotting points (1, 0), (-2, 1) and (4, -1) joining them, we get a line l₁ which is the graph of equation (i).

Again, 5x + 1 = 4x - y + 2     ....(ii)
⇒ x = 1 - y
Corresponding values of x and y can be tabulated as :

x	-1	3	-2
y	2	-2	3

Plotting points (-1, 2), (3, -2) and (-2, 3) joining them, we get a line l₂ which is the graph of equation (ii).

The two lines l₁ and l₂ intersect at a point P(1, 0).
∴ x = 1, y = 0 is the solution of the given system of equations.
Since both the lines l₁ and l₂ are intersecting each other at X-axis, no triangle is formed by these lines with X-axis.