What is the result of subtracting the second equation from the first?

Question

-2x+y=0

-7x+3y=2

Answer 1

Changes made to your input should not affect the solution:

 (1): "y2" was replaced by "y^2". 

Step by step solution :

Step 1 :

Equation at the end of step 1 :

 3y² - y = 0

Step 2 :

Step 3 :

Pulling out like terms :

 3.1    Pull out like factors :

   3y² - y  =   y • (3y - 1) 

Equation at the end of step 3 :

 y • (3y - 1) = 0

Step 4 :

Theory - Roots of a product :

 4.1   A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

 4.2      Solve  :    y = 0 

 Solution is y = 0

Solving a Single Variable Equation :

 4.3      Solve  :    3y-1 = 0 

 Add 1 to both sides of the equation : 

                      3y = 1

Divide both sides of the equation by 3:

                     y = 1/3 = 0.333

Two solutions were found :

1.  y = 1/3 = 0.333
2.  y = 0