Determine which system below will produce infinitely many solutions.
a. -6x+3y=18
4x-3y=6
b. 2x+4y=24
6x+12y=36
c. 3x-y=14
-9x+3y=-42
d. 5x+2y=13
-x+4y=-6
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The answer is the option C

Step-by-step explanation:

case A) we have

------> equation A

------> equation B

Adds equation A and equation B

Find the value of y

substitute in the equation A the value of x

therefore

the system case A) has one solution

case B) we have

------> equation A

------> equation B

Multiply by equation A

so

Equation A and equation B are parallel lines

therefore

the system case B) has no solution

case C) we have

------> equation A

------> equation B

Multiply by equation A

------->

Equation A and equation B are the same line

therefore

the system case C) has infinitely solutions

case D) we have

------> equation A

------> equation B

Multiply by equation B

-------> equation C

Adds equation A and equation C

Substitute the value of y in the equation B

the system case D) has one solution

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

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