How many solutions does the system of equations have?
4x+16y=12
y=-1/4x+9/12
a. one
b. two
c. infinitely many***
d. none
One, they're both lines with a different coefficient so they'll only cross once.
That was a lie btw, they won't cross so d. their coefficient IS the same.
4x+16(-1/4x + 9/12) = 12
4x -4x + 12 = 12
0 = 0
they overlap
so C.
IGNORE PAST ANSWERS
the lines are the same, infinite solutions.
To determine the number of solutions for the given system of equations, we can examine the slopes and y-intercepts of the equations.
The first equation, 4x + 16y = 12, can be simplified by dividing by 4, resulting in x + 4y = 3. To find the slope-intercept form of this equation, we can isolate y:
x + 4y = 3
4y = -x + 3
y = -1/4x + 3/4
Comparing the second equation, y = (-1/4)x + 9/12, with the simplified form of the first equation, we see that both equations are the same. This means that the system of equations is actually just one equation written in two different forms.
Since both equations represent the same line, they have infinitely many points of intersection. Therefore, the correct answer is c. infinitely many.