Classify the system and give the number of solutions.

Question

{-2y+2x=3

{-5y+5x=12

Answer 1

This system of equation is inconsistent: it has no solution.

 

{-2y+2x=3
{-5y+5x=12

 

Check the determinant: (-2*5) - (-5*2) = 0

 

Another way to check the answer is by using online system equations solver: http://examn8.com/SystemOfEquations.aspx

 

Hope this helps. 

Answer 2

-2y + 2x = 3
-5y + 5x = 12

 

Let us change both of these to the form y = mx + b, where m = slope and b = y intercept

 

-2y + 2x = 3 

-2y = -2x + 3

y = (-2/-2)x + 3/(-2)

y = x - 3/2

 

-5y + 5x = 12

-5y = -5x + 12

y = (-5/-5)x + 12/(-5)

y = x - 12/5

 

Our 2 equations are

 

y = x - 3/2

y = x - 12/5

 

Note they have the same slope, so they are parallel lines.  They have different y-intercepts, so they are different lines.  There is no intersection, i.e. no pair (x,y) that satisfies both equations, hence no solution.

 

 

 

 

Answer 3

The slopes and y-intercepts are different. The system is consistent. The system has one solution.