This question is from linear equations in two variables in which we have been asked to solve the equations graphically and also asked to find the vertices and the area of the triangle formed by these lines and the x-axis if the given equations are x-y+1=0, 3x+2y-12=0

RS Aggarwal, Class 10, chapter 3A, question no 14

## xâˆ’y+1=0….(1)

3x+2yâˆ’12=0……(2)

IsolateÂ xÂ from equation (1) and find the value ofÂ xÂ andÂ y.

xâˆ’y+1=0

orÂ x=yâˆ’1

Similarly, isolateÂ xÂ from equation (2) and find the values ofÂ xÂ andÂ y.

3x+2yâˆ’12=0

orÂ x=(12âˆ’2y)/3

Graph:

Both the lines intersect each other at pointÂ E(2,3)Â andÂ xâˆ’Â axis atÂ A(âˆ’1,0)Â andÂ D(4,0)

To find the area of triangleÂ BAD:

Area ofÂ â–³EAD=1/2(baseÃ—altitude)

=1/2Ã—5Ã—3

=7.5Â sq.units.