Question

PLEASE HELP ASAP IM GIVING AWAY FREE POINTS PLUS BRAINLIEST FOR CORRECT ANSWER!!!!

Which answer describes the graph of the system of equations?

{y = 4-x
{2y = 8 - 2x

A. The point of intersection is (0, 4).

B. The point of intersection is (4, 0).

C. The lines are parallel.

D. The lines coincide.

Answer 1

Answer:

D. Lines coincide

Step-by-step explanation:

On dividing y/2y and 4/8 and x/2x you get 1/2. Since 1/2 is common answer for all the parts, lines will coincide.

Answer 2

Answer:

D. The lines coincide.

Step-by-step explanation:

Since, a system of two lines $a_1x+b_1y=c_1$ and $a_2x+b_2y=c_2$,

Has a point of intersection, if,

$\frac{a_1}{a_2}\neq \frac{a_2}{b_2}$

Has infinitely many solution ( i.e. lines are coinciding ), if,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Has no solution ( i.e. lines are parallel ), if,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}$

Here, the given system of equations,

y = 4 - x ⇒ x + y = 4,

2y = 8 - 2x ⇒ 2x + 2y = 8

$\because \frac{1}{2}=\frac{1}{2}=\frac{4}{8}$

Thus, by the above explanation,

The given lines coincide.

Option 'D' is correct.