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Mariulka [41]
3 years ago
14

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
Mathematics
1 answer:
Elden [556K]3 years ago
3 0

Given:

The first equation of the system of equations is

5x+2y=-4

To find:

The equation that gives a system with no solution.

Solution:

We have,

5x+2y=-4

It can be written as

2y=-5x-4

y=\dfrac{-5x-4}{2}

y=-\dfrac{5}{2}x-2

On comparing this equation with slope intercept form y=mx+b, we get

m=-\dfrac{5}{2},b=-2

It means the slope of the line is -\dfrac{5}{2} 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 -\dfrac{5}{2} only in option D and the y-intercept is -3 which is different from -2.

The line y=-\dfrac{5}{2}x-3 is parallel to the given line and parallel lines have no solution. So, the second equation of the system of equations is y=-\dfrac{5}{2}x-3.

Therefore, the correct option is D.

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