Question

100PTS PLEASE GIVE EXPLANATION

(I really need help please)

2x + 6y= 12

X + 3y= 6


In solving the system of equations shown above, Sean showed the following steps:

Step 1: x = 6 – 3y

Step 2: 2(6-3y) + 6y = 12

Step 3: 12 – 6y + 6y = 12

Step 4: 12 = 12


Sean’s work is correct. However, there are no variables in Sean’s final step. What can he state as the solution of the system?

Answer 1

Explanation:

There are two equations in the question

`2x+6y=12\ -->Equation\ 1\\\\x+3y=6\ -->Equation\ 2\\\\`

If we take 2 common from the first Equation it becomes,

`2(x+3y)=12\\\\x+3y=12/6\\\\x+3y=6\\`

Now we can see that both the Equations are similar which means they would have the same graph.

Since both the equations have the same equation of line they have infinitely many solutions which means both the lines intersect at each and every point on the line, since both the lines are on top of each other.

We can also see that in Step 4 where 12 = 12 there are no variables in the equation which also means that the work is correct and Sean can say that the system of equations is consistent and dependent which means they have infinite number of solutions

Answer 2

The system has infinitely many solutions

Explanation:

There are no variables left. And the final equation is correct.

It means the system is going to be correct for any value of variables. So there are infinitely many solutions