helps solving systems of equations

Question

please solve the systems of equations.  If it cannot be solved, please explain why.

 

 

1.  3x + y = 7

     3x + y = 10

 

 

2.  5x - 2y = -24

         -4y = -48 - 10x

Answer 1

 3X + Y = 7

 

 3X + y =10

 

  subtracting  2 equations from each other , the result will be 0 equal  3 or -3 , that indicates  no solution.

 

 Y = -3X +7

 

 Y = -3x +10

 

    You see that both lines have same slope , but different Y -intercept, therefore; line are parallel and no intersecting points.

 

  System of equation of as such is called  INCONSISTENT .

Answer 2

The equations in 1. are the same except for the constant term so they represent parallel lines with no solutions.

 

In 2. the 2nd equation can be manipulated into 5x - 2y = -24, the same as the 1st equation. So this system describes the same single line. Every point on the line is a solution to both equations, so there are an infinite number of solutions.