Question

Solve the equations graphically. 2x+y=2 , 2y-x=4. Also find the area of a triangle formed by the two lines and the line y=0.

Answer 1

multiply 2x+y=2 with 2 to get the equation 4x+2y=4.(equation 1)
subtract it from the  equation -x+2y=4 (equation 2)
you get 5x=0
now substitute zero in place of x in equation 1.
you get y=2
that is the solution of the two lines.
now substitute some random values in place of x and y in the equation that satisfy the equation.


now draw two separate line for the two equations respectively.

y=0 is a line which is passing through the x-axis
its equation is 0x+y=0

(for reference: http://kwiznet.com/p/takeQuiz.php?ChapterID=10634&CurriculumID=42&Num=1.15)


for the area of the triangle you can use the formula 1/2|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)| to get the answer

$\left[\begin{array}{cccc}x1&x2&x3&x1\\y1&y2&y3&y1\\\end{array}\right]$

or


HERON'S formula
 by finding individual distance between the vertices of the triangle