Precalculus, Chapter 7, 7.2, Section 7.2, Problem 24

7x+8y=6
-14x-16y=-12
From the first equation,
7x=6-8y
x=(6-8y)/7
Substitute the value of x obtained in the second equation,
-14((6-8y)/7)-16y=-12
-2(6-8y)-16y=-12
-12+16y-16y=-12
-12+0y=12
The equations has an infinite number of solutions.
If the equations are of the form,
a_1x+b_1y+c_1=0
a_2x+b_2y+c_2=0
and if,
a_1/a_2=b_1/b_2=c_1/c_2
then the equations have an infinite number of solutions.