HELP. What is the value of y in the solution to the following system of equations? MULTIPLE CHOICE.

2x + y = −4
5x + 3y = −6

A. 6
B. 8
C. −6
D. −8

2x + y = -4
5x + 3y = -6

What you must do is find one of the variables. Since it's easier to find y, let's solve for y in the first equation:

2x + y = -4
y = -4 - 2x

Now you plug this value of y into the second equation:

5x + 3(-4 - 2x) = -6
5x - 12 - 6x = -6
-x - 12 = -6
-x = 6
x = -6

Now you have x, so you can take this value of x and plug it back into the first equation, and solve for y:

2x + y = -4
2(-6) + y = -4
-12 + y = -4
y = -4 + 12
y = 8

Solution: B. y = 8

take 2x + y = −4

and solve for y

y = -2x - 4

plug this value into 5x + 3y = −6

to get

5x + 3(-2x - 4) = -6

5x - 6x - 12 = -6

-x = 6

x = -6

now plug this back into the first equation

2(-6) + y = −4

-12 + y = -4

y = 8

B is the correct answer

call the top equation 1 and the bottom equation 2.

rearrange equation 1

y = -4 - 2x

substitute in equation 2

5x + 3(-4 - 2x) = -6

5x -12 - 6x = -6

5x-6x = -6+12

-x = 6
x = -6

substitute back in equation 1

2(-6) + y = -4

-12 + y = -4

y = -4 + 12

y = 8

Answer is B.

Solve by elimination.

2x + y = -4 multiply by -3=> -6x -3y = 12
5x + 3y = -6 stays the same=> 5x + 3y = -6
-----------------
-x = 6
x = -6
Solve for y.
2(-6) + y = -4
-12 + y = -4
y = 8

So the answer is B.

Eqn1x5: 10x + 5y = -20
Eqn2x2: 10x + 6y = -12
subtract: y = 8 so B <---- Ans

(b) 8

B

b