Question

Plot the graph of the following system of equations 3x+y=11; x-y=1​

Answer 1

Answer:

18sq.units

Step-by-step explanation:

 3x+y-11= 0

=> y= 11-3x

If x= 0,   y= 11-3*0= 11

If x= 3,   y= 11-3*3= 2

x-y-1= 0

y= x-1

If x= 0,    y= 0-1= -1

If x= 3,    y= 3-1= 2

The Two lines intersect in the point A (3,2). Hence, x=3 and y=2 is the solution of the equation.

The lines represented by the other two equations meet at y-axis at B (0,11) and C (0,-1) respectively.

Draw AD perpendicular to y-axis.

AD= x- coordinate of point A (3,2)

AD= 3

BC= 11-(-1)= 12

Area of the Shaded Area= Area of the Triangle

$A=\frac{1}{2} *BC*AD$

$=\frac{1}{2} *12*3$

= 18sq.units