Question

Which of these steps will eliminate a variable in this system?

4x - 9y = 8
2x + 3y = 24

A. Multiply the first equation by 3. Then subtract the second equation from the first.

B. Multiply the second equation by 2. Then add the equations.

C. Multiply the second equation by 2. Then subtract the second equation from the first.

D. Multiply the second equation by 3. Then subtract the second equation from the first.

Answer 1

option c is correct

Explanation:

for any variable to be eliminated in a simultaneous equation, the one of the coefficients must be the same in the two equations. and:

FOR OPTION A

if the first equation is multiplied by 3 , we will be having 12x-27y= 24 as the new equation 1 and since the cofficient of y or x are different in equation 1 and 2, no variable can be eliminated.

FOR OPTION B

if the second equation is multiplied by 2, our new equation 2 will be 4x+6y= 48. here, the cofficient of x in the two equations are now the same but since we're going to add, 4x+4x = 8x which does not eliminate x

FOR OPTION C

if the second equation is multiplied by 2, our new equation 2 becomes 4x + 6y= 48 and if we subtract, 4X-4x= 0 so we have eliminated X ( option C is correct)

FOR OPTION D

if the second equation is multiplied by three, our new equation 2 becomes 6x+9y= 72 and subtracting,-9y -9y= -18y which does not eliminate y