10y - 3x = - 41 [1]
3x - 5y = 16 [2]
So we can rearrange the equation [2] :
3x - 5y = 16
Add 5y to both sides of the equation:
3x - 5y + 5y = 16 + 5y
3x = 16 + 5y
We can now substitute this into equation [1] :
So, 10y - 3x = - 41 , becomes:
10y - (16 + 5y) = - 41
10y - 16 - 5y = - 41
5y - 16 = - 41
Now add 16 to both sides of the equation:
5y - 16 + 16 = - 41 + 16
5y = - 25
Now you can divide both sides of the equation by 5 to find the value of y:
5y/5 = - 25/5
y = - 5
You can now substitute this value into either equation [1] or [2]. I will choose [2]:
So, 3x - 5y = 16 , becomes:
3x - 5(-5) = 16
3x - (- 25) = 16
3x + 25 = 16
Now we can subtract 25 from both sides of the equation:
3x + 25 - 25 = 16 - 25
3x = - 9
Now we can divide both sides of the equation by 3:
3x/3 = - 9/3
x = - 3
So the solution to the equation is:
x = - 3 and y = - 5