which of the linear systems has no solution?

Question

A. -x+y=1/2     y=x+3/4

 

B.  y=1/4x+2    -x+4y=8

 

C.  2x+3y=18   y=-3/2x+6

 

D.  y=-2/3x+1/3   4x+6y=2

 

Please show how you get it. 

Answer 1

Suppose we graph two linear equations on the same coordinate system, they will share a common point when they intersect.  That point of intersection is the solution to the set of equations.  However, only equations whose lines have different slopes will intersect.  This means that a set of lines which are parallel will never intersect, thus having NO solutions. 

 

To do this, we put each set of equations in the y=mx+b form, where m is slope and b is y-intercept.  Compare their slopes for each answer choice.

 

 

Answer 2

A) both lines have slope of 1. You can see this by writing both equations in the standard

 

  y=mx+b form

 

lines with the same slope (m) but different y intercepts (b) are parallel. They do not intercept  there is no solution. 

 

B) These equations describe the same line writing in standard format you can see they have the same slope and the same y intercept.  There are an infinite number of points that satisfy both equations. 

 

C) These are two distinct lines. To find their intercept plug the second equation into the first. 

 

2x+3(-3x/2+6)=18

2x-9x/2+18=18

x=0 plugging this into either equation 

y=6

 

D)Is like B they describe the same line

 

The answer is A the parallel lines do not intercept. They have no solution