How many solutions does the following system of equations have?

Question

How many solutions does the following system of equations have?

  y-5/x+2     <----equation
2y=5x+4     <----equation

One
Two
Zero
Infinitely many

Answer 1

The given equations are

 

    y = 5/x + 2

 

    2y = 5x + 4

 

We can substitute "5/x + 2" for y in the second equation, and then solve for the varuable

 

    2(5/x + 2) = 5x + 4

 

    10/x + 4 = 5x + 4

 

Multiply all terms by x to clear the fractions

 

    10 + 4x = 5x² + 4x

 

Subtract 4x from both sides

 

     10 = 5x²

 

Divide both sides by 5

 

     5 = x²

 

     x² = 5

 

     x = ±√5

 

Thus there are 2 solutions