Question

How many solutions does the following system of equations have
4x-20y=-16
2x-10y=-8

Answer 1

Answer: infinite number of solutions

Explanation:

The second equation is basically doubled the first equation.

4x-20y=-16---------> 4x-20y=-16-------->4x-20y=-16

-2(2x-10y)= -2(-8)----> -4x + 20y=16-->-4x+20y=16

Add down and you get 0=0 or in other words, infinite number of solutions.

Answer 2

Explanation:

you know how fractions can be reduces, well, so can equations.

4x - 20y = -16......reduce by dividing by 4

x - 5y = -4

2x - 10y = -8....reduce by dividing by 2

x - 5y = -4

same line......INFINITE SOLUTIONS

or u can do it this way also.....put them in y = mx + b form

4x - 20y = -16

-20y = -4x - 16

y = 1/5x + 4/5......slope is 1/5 and y int is 4/5

2x - 10y = -8

-10y = -2x - 8

y = 1/5x + 4/5.....slope is 1/5 and y int is 4/5

same slope, same y int, means same line with infinite solutions