Solve the simultaneous equations in Z24,
3x+4y=18
12x+7y=4
Thanks!
1st times 4 --> 12x + 16y = 72
2nd as is ----> 12x + 7y = 4
subtract them:
9y = 68
y = 68/9
back in 1st:
3x + 4(68/9) = 18
3x = 18 - 272/9 = -110/9
x = -110/27
To solve the simultaneous equations in Z24, we'll start by rearranging the equations to solve for one variable in terms of the other and then substitute the value back into the other equation.
Let's solve for x in terms of y from the first equation:
3x + 4y = 18
3x = 18 - 4y
x = (18 - 4y)/3
Now substitute this value of x into the second equation:
12x + 7y = 4
12((18 - 4y)/3) + 7y = 4
4(18 - 4y) + 7y = 4(3)
72 - 16y + 7y = 12
72 - 9y = 12
-9y = 12 - 72
-9y = -60
y = (-60)/(-9)
y = 20/3
Now we have the value of y. Let's substitute it back into the first equation to find x:
3x + 4(20/3) = 18
3x + 80/3 = 18
3x = 18 - 80/3
3x = (18*3 - 80)/3
3x = (54 - 80)/3
3x = (-26)/3
x = (-26/3)*(1/3)
x = -26/9
So the solution to the simultaneous equations in Z24 is:
x = -26/9
y = 20/3