Question

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

Answer 1

A

Explanation:

-6 and 6

Answer 2

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

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.