How do you solve the system of equations -6x + 5y = - 5 and 10x - 10y = 20?

1 Answer
Jun 6, 2018

x=-5 and y=-7.

Explanation:

For this system of equations, I would adjust the first equation so that when you add the two equations together, the y is eliminated.

You can do so by multiplying everything by 2:

(-6x+5y=-5)" " times 2

-12x+10y=-10

Now that this equation has a positive 10y and the other equation has a -10y, adding the two problems would eliminate the y variable.

{(-12x+10y=-10), (10x -10y= 20) :}

Added together:

-2x=10

You can now solve for x by dividing both sides by -2.

x=-5

Now you can take any of the equations and enter in -5 for x to solve for y.

-6(-5)+5y=-5

Multiply the -6 and -5

30+5y=-5

Subtract 30 from both sides

5y=-35

Divide both sides by 5

y=-7

There are many ways to solve systems of equations, but often it's easiest to find a way to adjust one of the equations so that when you add them together they eliminate one of the variables.