# When solving (2x+y=4 and x+y=10)  by substitution,  arrived at ( -y = -16). Can I multiply each side by (-1) to achieve a positive result?

txmedteach | Certified Educator

That is exactly what you do! When solving an equation, as long as you do exactly the same thing to both sides, you can do whatever you want, and both sides will equal each other.

This includes multiplying both sides in this case by -1 to get y = 16.

You might be mixing this up with an inequality, where you would have to flip the sign. For example, if you had -y > -16, solving for y would give you y < 16.

It's interesting you're using substitution to solve this equation, though. To me, elimination looks like the easiest way. Subtracting the second equation from the first yields x = -6. From this, you can easily find y = 16.

Hope that helps!

tonys538 | Student

To solve (2x+y=4 and x+y=10)  by substitution, using the equation x+y=10 we get x = 10 - y. If this is substituted in 2x + y = 4, we get

2*(10 - y) + y = 4

20 - 2y + y = 4

-y = -16

Now in an equation it is possible to add or subtract both the sides of the equation by any number and not change the equation. Similarly, both the sides can by multiplied by or divided by any non-zero number without altering the equation.

In the given problem

-y = -16 is the same as : -y*-1 = -16*-1

y = 16

As x + y = 10

x = 10 - 16 = -6

malkaam | Student

An important rule of algebra is what happens to one side also has to happen to the other side as well.  So the answer is yes you have to multiply both sides by -1 to get a positive answer.

-y = -16

-1(-y) = -1(-16)