MATH SOLVE

4 months ago

Q:
# Two lines, A and B, are represented by the following equations:Line A: 4x + 4y = 16Line B: x + y = 4Which 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.

Accepted Solution

A:

The correct answer is: [B]:

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"There are infinitely many solutions."

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(e.g. (0, 4), (1, 3), (-1, 5), (-2, 6), (-3, 7), (2, 2), (3, 1) ...

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Note:

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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 .

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___________________________________________________

"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 .

___________________________________________