a system of equations and the solution are shown 6x+3y=6 4x-2y=4 solution: (1,0)

Question

select the equation equivalent to the first equation in the system such that when added to the second equation a system with the same solution as the original system is formed

Answer 1

To find an equivalent equation to 6x + 3y = 6, we can simply multiply every term in the equation by a constant. Let's choose to multiply by 2:

2(6x + 3y) = 2(6)
12x + 6y = 12

Now, if we add this new equation to the second equation in the original system, we will get a system with the same solution as the original system:

12x + 6y + 4x - 2y = 12 + 4
16x + 4y = 16