How do you solve 6x-2y equals -16 4x plus 4y equals -32?

Answer 1

x = -4 and y = -4.

These are known as simultaneous equations. We have to manipulate the equations in order to remove one of the variables. Then we can solve for the remaining variable. Once we have done this, we can substitute this value back into one of the original equations to solve for the other variable. So:

1. 6x - 2y = -16

2. 4x + 4y = -32

If we multiply 1. by 2 then we will end up with a -4y in one equation and 4y in the other. We will then be able to add these together which will cancel out and remove the y variable altogether.

So, 1. multiplied by 2 gives:

3. 12x - 4y = -32

Adding 2. & 3. gives:

4. 16x = -64

x = -64/16

x = -4

Now we have worked out the value of x we can substitute this value back into one of the original equations.

Substituting x = -4 back into 1. gives:

(6 * -4) - 2y = -16

-24 - 2y = -16

2y = -24 + 16

2y = -8

y = -4

We can double check we have solved this correctly by substituting both values into the other original equation.

Substituting x = -4 & y = -4 into 2. gives:

(4 * -4) + (4 * -4) = -32

-16 + -16 = -32

-32 = -32 (Yes this works, we have found the correct values of x & y!)