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Rewrite the equation [tex]x + y + 3 = -2x + 4y + 18[/tex] into general form ([tex]ax + by + c = 0[/tex]).

A. [tex]x + y - 5 = 0[/tex]

B. [tex]3x - 3y - 5 = 0[/tex]

C. [tex]x - y - 15 = 0[/tex]

D. [tex]x - y - 5 = 0[/tex]

Sagot :

GinnyAnsweridn
To rewrite the equation [tex]\( x + y + 3 = -2x + 4y + 18 \)[/tex] into the general form [tex]\( ax + by + c = 0 \)[/tex], we should follow these steps:

1. Move all terms to one side of the equation:
[tex]\[ x + y + 3 + 2x - 4y - 18 = 0 \][/tex]

2. Combine like terms:
[tex]\[ (x + 2x) + (y - 4y) + (3 - 18) = 0 \][/tex]
[tex]\[ 3x - 3y - 15 = 0 \][/tex]

Thus, the general form of the equation is:
[tex]\[ 3x - 3y - 15 = 0 \][/tex]

Now, let's compare this equation to the provided options:

A. [tex]\( x + y - 5 = 0 \)[/tex]

B. [tex]\( 3x - 3y - 5 = 0 \)[/tex]

C. [tex]\( x - y - 15 = 0 \)[/tex]

D. [tex]\( x - y - 5 = 0 \)[/tex]

The correct answer is B:
[tex]\[ 3x - 3y - 15 = 0 \][/tex]
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