The first equation in a system is 5x + 2y = –4. Which equation gives a system with no solution? A. y = 2x + 6 B. y = 1/4x – 2 C. y = 2x + 7 D. y = –5/2x – 3

Given:

The first equation of the system of equations is

To find:

The equation that gives a system with no solution.

Solution:

We have,

It can be written as

On comparing this equation with slope intercept form , we get

It means the slope of the line is and the y-intercept is -2.

Slope of parallel lines are same but the y-intercepts are different.

From the given options, the slope of the line is only in option D and the y-intercept is -3 which is different from -2.

The line is parallel to the given line and parallel lines have no solution. So, the second equation of the system of equations is .

Therefore, the correct option is D.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

step-by-step explanation: