Question

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

Answer 1

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)

Answer 2

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