Which of these systems of linear equations has no solution?

A) 2 x + 8 y = 15. 4 x + 16 y = 30.

B)2 x- y = 18. 4 x + 2 y = 38.

C)4 x + 7 y = 17. 8 x -14 y = 36.

D)4 x -3 y = 16. 8 x -6 y = 34.

D)4 x -3 y = 16. 8 x -6 y = 34.

Step-by-step explanation:

A system of linear equations is a set of (linear) equations that have more than one unknown. The unknowns appear in several of the equations and these equations relate the unknowns or variables to each other.

When you solve a system of two equations with two unknowns, what you are really doing is finding the cut-off point of the two lines, if any. But if the graphs of the equations do not intersect, then there is no solution to the equations. In this case the lines are parallel and the system is incompatible. The lines are parallel when they have the same slope, but different ordinate. The way to represent a line is

y= mx+n Equation (A)

where m is the slope and n is the ordinate.

In this case, subsection D) is a system without solution. To observe this, you first express as equation (A) the lines:

4x - 3y=16     ⇒     -3y=16 -4x     ⇒ y= -16/3+4/3 x

8 x -6 y = 34    ⇒    -6y=34-8x    ⇒    y=-17/3 +4/3 x

 You can see that the lines are parallel because they have the same slope. Then it will be a system without solution. You can also see it in the attached graph, where the green line belongs to the line 4x -3y=16 and the red line to the line 8x -6y=34