The second equation gives you an expression you can modify to substitute for the variable y in the first equation as follows:
3x + y = 0
3x + y - 3x = 0 -3x
y = -3x
Then substitute this expression for y in the first equation as follows:
-x - 2y = -5
-x - 2(-3x) = -5
This is equivalent to :
-x + 6x = -5
Now combine like terms and use inverses operations to determine the value of x (Note : -x + 6x is equivalent to 5x) :
5x = -5
5x/5 = -5/5
x = -1
Use the second equation to determine the value of y:
3x + y = 0
3 * (-1) + y = 0
-3 + y = 0
-3 + y + 3 = 0 + 3
y = 3
Therefore the solution to the system of equations is (-1, 3)
If you substitute these values into either equation, you will see that x = -1 and y = 3 satisfies both equations.
