Question

Solve the following system of equations graphically:
2x = 23 - 3y
5x = 20 + 8y
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 2x = 23 - 3y and 5x = 20 + 8y.
Now, 2x = 23 - 3y    ....(i)

⇒ x = `(23 - 3y)/(2)`
Corresponding values of x and y can be tabulated as follows :

x	10	7	4
y	1	3	5

Plotting points (10, 1), (7, 3) and (4, 5) joining them, we get a line l₁ which is the graph of equation (i).

Again, 5x = 20 + 8y    ....(ii)
⇒ x = `(20x + 8y)/(5)`
Corresponding values of x and y can be tabulated as follows :

x	4	2.4	0.8
y	0	-1	-2

Plotting points (4, 0), (2.4, -1) and (0.8, -2) 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(7.8, 2.4).
∴ x = 7.8, y = 2.4 is the solution of the given system of equations.
Draw PM perpendicular from P to X-axis.
Now, PM = y-coordinate of P(7.8, 2.4)
⇒ PM = 2.4 units
QR = 11.5 - 4
= 7.5 units
∴ Area of ΔPQR

= `(1)/(2) xx "QR" xx "PM"`

= `(1)/(2) xx 7.5 xx 2.4`
= 9 sq. units.