What is the solution set of the given system?

Question

2y = x + 3 and 5y = x - 7

Answer 1

Given equations are 2y = x + 3 and 5y = x - 7

                             => x = 2y - 3

Substitute x = 2y -3 in 5y = x - 7 we get,

                             => 5y = x - 7

                             => 5y = 2y - 3 -7

                             => 5y - 2y = -10

                             => 3y = -10

                             => y = -10/3

Substitute y value in x = 2y - 3 we get,

                            => x = 2(-10/3) - 3

                                    = (-20 -9)/3

                                    = -29/3

Therefore x = -29/3 and y = -10/3

                        

Answer 2

The given equations 2y = x+3  -> (1) and  5y = x -7  ->(2)

Add -2y to each side

x - 2y +3 = 0

Add -5y to each side

x - 5y -7 = 0

Solving for equations

x -2y +3 = 0

x -5y - 7 = 0

-------------------

3y+10 = 0

Therefore y = -10/3

Substitute y value in equation (1)

2( -10/3) = x+3

-20/3 = x+3

x = (-20/3) -3

Therefore x = -29/3

The solution is x = -29/3 and y = -10/3.