This answer is done through substitution.
Use 2x+y = 0
y = -2x
Now, use this y value and substitute in the 1st equation
4x + 3 (-2x) = 21
4x + -6x = 21
-2x = 21
x = - 21/2
x= -10.5
Now, use this value into 1st equation again to find y
4(-10.5) + 3y = 21
-42 + 3y = 21
3y = 21 + 42
3y = 63
y=63/3
y=21
Use this and the value of X we got above to substitute in the 2nd equation.
2 (-10.5) + 21
=-21 + 21 = 0
The answer is zero.
If you want to keep the fraction and not use a decimal, you can do so from the previous steps. Still you will get the same answer.