How many solutions does the system of equation have? 4x + 16y = 12 y = -1/4x + 9/12 a. one b. two c. infinitely many d. none

The equation no solution. This is because the lines are parallel.
The general equaltion of a line is,

Y=mX+c, where m is the gradient and c is the Y-intercept.

For the first equation,
4x + 16y = 12
16y=-4x+12
y=(-1/4)x+12/16
gradient =-1/4

For the second equation, Y = (-1/4)x +9/12,  the gradient = -1/4
 If the gradients are equation then, the lines do not meet hence no solutions.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.