Consider this system of equations and the partial solution below

6x+2y = 6

7x+3y - 9

Multiply the first equation by - 3.

Multiply the second equation by 2

Add the resulting system of equations,

Which terms will cancel when you add the resulting system of equations?

A. - 6y and 6y

B. - 14x and 14x

C. - 32 and 32y

D. - 18x and - 18

A

Step-by-step explanation:

-6 and 6

A. - 6 y and 6 y terms will cancel when we add the resulting system of equations.

Step-by-step explanation:

Here, the system of equations is given as:

6 x + 2 y = 6 ... (1)

7 x + 3 y = 9 ... (2)

Now, multiplying (1) by (-3), we get

(-3) 6 x + (-3) 2 y = (-3) 6

⇒ - 18 x - 6 y = - 18

And, multiplying (2) by (2), we get

(2) 7 x + (2) 3 y = (2) 9

⇒ 14 x + 6 y = 18

Now, adding both the resulting equations, we get

(-18 x - 6 y) + (14 x + 6 y) = - 18 + 18

or, (-18 x + 14 x) + (6 y - 6 y) = - 18 + 18

or, - 4 x = 0

Hence, the terms + 6 y is cancelled with - 6 y in Left side

and term 18 is cancelled with - 18 on Right Side.

Hence, the option A. is the correct option.