How many solutions does this system have? 2x + y = 3

Question

6x = 9 – 3y

Answer 1

This system of equations has an infinite number of solutions. In fact, the first equation can be rewritten as y = 3 - 2x. Substituting this into the second equation gives 6x = 9 - 3(3 - 2x), which simplifies to 6x = 9 - 9 + 6x. This shows that the two equations are equivalent, meaning that the second equation is always satisfied if the first equation is satisfied. Therefore, there are infinitely many values of x and y that satisfy both equations.