what is the common for 5y - 5x = -5 and y = 2x - 5

Answer 1

substitute: 5(2x-5)-5x=-5

10x-25-5x=-5

5x-25=-5

5x=20

x=4

Answer 2

To find the common solution for two equations, you can use a strategy called elimination. If you can narrow one of the equations down to have only one variable isolated on one side, then you can substitute that equation into the other, and you'll only be working with one variable.

In your example, you already have a variable isolated in one of the equations -> y = 2x - 5.

So you can plug in "2x - 5" into the other equation for "y" (since the first equation says that 2x - 5 IS y).

5y - 5x = -5

5(2x-5) - 5x = -5 -> from here solve the equation like normal for the variable you have left, x.

10x - 25 - 5x = -5

5x = 20

x = 4

Now you can use x to find y by plugging your value into either equation

y = 2x - 5

y = 2(4) - 5

y = 8 - 5

y = 3

Therefore the common solutions for the two equations are x = 4 and y = 3. You can check this by plugging the values into both equations and seeing that they make sense.