Question

Show graphically that each one of the following systems of equations has infinitely many solutions:
$3x+y=8$
$6x+2y=16$

Answer 1

x	1	3
y	5	-1

Graph of the given equations:

Both lines have same x-intercept and same y-intercept

x-intercept =$\frac{8}{3}$

y-intercept =6

And both lines have same Slope

Slope =$\frac{-3}{1}=\frac{-6}{2}$

$\Rightarrow$both lines coincide and therefore they have infinite intersection points

$\therefore$this system has infinite solutions