Answer:
3/4 and -3/4
or
0.75 and -0.75
but there is no solution for
10 times the smaller number added to 6 times the larger number to get 3 as result.
the absolute values of x and y must be equal and with opposite signs (due to their sum being 0).
therefore, 10 times the negative value can never be compensated by 6 times the same but positive value. the sum will always be negative and not positive (and therefore not +3).
it only works with 10 times the larger (positive) number plus 6 times the smaller (negative) value.
Step-by-step explanation:
x + y = 0
10×x + 6×y = 3
=>
x = -y
10×(-y) + 6×y = 3
-10y + 6y = 3
-4y = 3
y = -3/4
=>
x = -y = -(-3/4) = 3/4
control :
10×(3/4) + 6×(-3/4) = 30/4 - 18/4 = 3
12/4 = 3
3 = 3
correct
