Question

Which of these strategies would eliminate a variable in the system of equations? { − x + 6 y = 8 7 x − y = − 2 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ −x+6y=8 7x−y=−2 ​ Choose all answers that apply:

Answer 1

Answer:c

Step-by-step explanation:

Answer 2

Answer:

The required solution is $x=\frac{98}{41}$  and $y =\frac{8}{123}$.

Step-by-step explanation:

Given equations are

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

$\frac87x-y=-2$.......(2)

First we have to equate the coefficient of y or x. Here we equate the coefficient of y . So equation (2) multiply by 6.

Then the equation (2) becomes

$\frac{8\times 6}{7}x-6y=-2\times6$

$\Rightarrow \frac{48}{7}x-6y=-12$........(3)

Since the signs of y are is opposite, so we adding (1) and (2).

$(-x+6y)+ \frac{48}{7}x-6y=-2-12$

$\Rightarrow -x+\frac{48}{7}x=-14$

$\Rightarrow \frac{-7x+48x}{7}=-14$

$\Rightarrow \frac{41x}{7}=-14$

$\Rightarrow x=\frac{-14\times 7}{41}$

$\Rightarrow x=\frac{98}{41}$

Putting the value of equation (1)

$-\frac{98}{41}+6y=-2$

$\Rightarrow 6y =-2+\frac{98}{41}$

$\Rightarrow 6y =\frac{-82+98}{41}$

$\Rightarrow y =\frac{16}{41\times 6}$

$\Rightarrow y =\frac{8}{123}$

The required solution is $x=\frac{98}{41}$  and $y =\frac{8}{123}$