Solve the following system of linear equations.

3x - 5y = - 39

6x + 2y = - 42

Select one:

A. (-2, - 14)

B. (-8, 3)

C. no solution

D. infinitely many solutions

B

given the 2 equations

3x - 5y = - 39 → (1)

6x + 2y = - 42 → (2)

multiply (1) by - 2

- 6x + 10 y = 78 → (3)

add (2) and (3) term by term to eliminate x

(6x - 6x) + (2y + 10y) = ( - 42 + 78)

12y = 36 (divide both sides by 12)

y = 3

substitute this value in either of the 2 equations and solve for x

(2) → 6x + 6 = - 42 (subtract 6 from both sides)

6x = - 48 (divide both sides by 6)

x = - 8

solution is ( - 8, 3) → B

To solve a problem like this, you will need to use substitution or elimination. For the sake of an example I will solve this using substitution.

First, solve one of the equations for x or y:

3x-5y=-39

3x=-39+5y

X = (-39+5y) / 3

Then substitute for the value of x in the second equation:

6x+2y=-42

6 ((-39+5y) / 3) + 2y=-42

Solve for y:

-78+10y + 2y=-42

-78+12y=-42

12y=36

Y=3

Once you've solved for y, you can plug in it's value to find x:

X=-39+5 (3) / 3

X=-24/3

X=-8

So, we can conclude that the correct answer is B. (-8,3)