Question

How many solutions does the system of equations have 4x+16y=12 y=-1/4x+9/12

Answer 1

The solution has no solutions because the slope is the same, but the y intercept is different hope this helps god bless

Answer 2

The first equation is ,

$4x+16y=12$

First we need to solve this equation for y , and for that we need to subtract 4x from both sides, that is

$16y = 12-4x$

Now we need to get rid of 16, and for that we have to divide both sides by 16, that is

$y= \frac{3}{4}-\frac{1}{4} x$

$y= -\frac{1}{4} x+\frac{3}{4}$

And the second equation is

$\\ y= -\frac{1}{4} x+\frac{9}{12}$

And on simplifying we will get

$y= -\frac{1}{4} x+\frac{3}{4}$

Which is same as the firrst equation. And in that case, there are infinite or many solutions .