Question

Solve the following pairs of equations graphically.
3x + y = 12
x - 3y = -6
Determine the co-ordinate of the vertices of the triangle so formed by the Y- axis line and X - axis , Also find its area.

Answer 1

$3x+y=k\Rightarrow x=0,y=k,y=0,x=4$

$x-3y=-6\Rightarrow x=0,y=2,y=0,x=-6$

$3x+y=k$

$3x+3y=-18$

_____________

$+++$

$10y=30$ $3x+3=k$

$y=3$ $3x=9$

$x=3$

Area $(3,3)(4,0)(-6,0)$

$△=\frac{1}{2}\left|\begin{array}{ccc}3& 3& 1\\ 4& 0& 1\\ -6& 0& 1\end{array}\right|$

$\left|\frac{1}{2}\left(3\right(0)-4(3-0)-6(3-0\left)\right]\right|$

$\left|\frac{1}{2}\right[3-k-18\left]\right|=\frac{27}{2}$ square Unit