Question

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

Line A: 4x + 4y = 16
Line B: x + y = 4

Which statement is true about the solution to the set of equations? (4 points)


It is (1, 2).


There are infinitely many solutions.


It is (1, 5).


There is no solution.

Answer 1

The correct answer is: [B]:
___________________________________________________
"There are infinitely many solutions."
___________________________________________________
(e.g. (0, 4), (1, 3), (-1, 5), (-2, 6), (-3, 7), (2, 2), (3, 1) ...
___________________________________________________
Note:
____________________________________________________
If we take the "first equation"; which is:

" 4x + 4y = 16 " ;

And divide "EACH SIDE of the equation by "4" ;


{4x + 4y) / 4 = 16 / 4 ;


→ 4x/4 + 4y /4 = 4 ;

→ x + y = 4 ;

which is the same as the "second equation" given:

→ x + y = 4 .
___________________________________________

Answer 2

Thew correct answer is that there are an infinite number of solutions.

Explanation:

You can find this by solving using elimination. To do this, multiply the bottom equation by -4 to get the x terms to cancel out. This leaves you with:

4x + 4y = 16

-4x - 4y = -16

When you add through, you are left with the expression:

0 = 0

When you get this using elimination, it means that there are an infinite number of solutions.