Question

Two lines, A and B, are represented by the following equations:

Line A: 3x + 3y = 12
Line B: x + y = 4

Which statement is true about the solution to the set of equations?


It is (12,4).
There are infinitely many solutions
It is (4,12).
There is no solution

Answer 1

There are infinitely many solutions.

Answer 2

Let's simplify equation Line A

3x + 3y = 12

3(x + y) = 3(4)

Divide 3 on both sides

x + y = 4

Now let's compare Line A and B again.

Line A: x + y = 4
Line B: x + y = 4

Both lines are exactly the same!

So that means any point that works in Line A should also work in Line B! That means it has infinitely many solutions! :)

Your answer is:
There are infinitely many solutions.

I hope that helps! :D