Question

what is the value of y in the following system of equations ? 2x + 3y = 6 2x + y = -2

Answer 1

y = 4

Step-by-step explanation:

2x + 3y = 6. #1

2x + y = -2. #2

Subtract Eq 2 from Eq 1,

3y - y = 6 - (-2)

2y = 8

or

y = 4

Answer 2

Answer:

y = 4

Step-by-step explanation:

2x + 3y = 6

2x + y = -2

Let's set the second equation equal to y. This means that y will be alone on one side of the equal sign.

2x + y = -2

Subtract 2x from both sides.

y = -2x - 2

Now that we have y as an expression, plug it into the first equation.

2x + 3y = 6

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

Distribute the 3 across the parentheses by multiplying.

2x - 6x - 6 = 6

Combine like terms.

-4x = 12

Divide both sides by -4.

x = -3

Now we have solved x.

To solve for y, plug x back into one of the equations.

y = -2x - 2

y = -2(-3) - 2

Multiply.

y = 6 - 2

Subtract.

y = 4

Check your answer by plugging both values back into the original equations.

2x + 3y = 6

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

Multiply.

-6 + 12 = 6

Add.

6 = 6

Your answer is correct.

Hope this helps!