Question

(08.01) 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

Answer: There are infinitely many solutions.

Step-by-step explanation:

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

Line A: 3x + 3y = 12

Line B: x + y = 4

By comparing to the equations $a_1x+b_1x=c_1$ and $a_2x+b_2x=c_2$ respectively , we have

$a_1=3,\ b_1=3\ \ \&\ c_1=12\\\\a_2=1,\ b_2=1\ \ \&\ c_2=4$

Now , $\dfrac{a_1}{a_2}=\dfrac{3}{1},\ \dfrac{b_1}{b_2}=\dfrac{3}{1},\ \&\ \dfrac{c_1}{c_2}=\dfrac{12}{4}=\dfrac{3}{1}$

i.e. $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$

It implies the gives lines are co-incident (linearly dependent).

That means it has infinitely many solutions.

So, the correct answer is "There are infinitely many solutions.".

Answer 2

Answer:

there are infinitely many solutions.

Step-by-step explanation:

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