1. 12x + 5y = 13
-24x - 5y = -11
First Add these equations to cancel out the y value so we can find the x value.
(12x + 5y = 13) + (-24x - 5y = -11)
= -12x + 0y = 2
Now we are left with the equation -12x = 2
Next divide both sides by -12 and x = -1/6
Now plug x into any of the original two equations to find the y-value.
12(-1/6) + 5y = 13
-2 + 5y = 13
5y = 15
y = 3
or
-24(-1/6) - 5y = -11
4 - 5y = -11
-5y = -15
y = 3
Sp, x = -1/6 and y = 3
2.-2x + 4y = 32
-5x - 10y = -20
First, lets simplify both of the equations.
(-2x + 4y = 32) / -2 = x - 2y = -16
(-5x - 10y = -20) / -5 = x + 2y = 4
Now we have the two equations:
x - 2y = -16
x + 2y = 4
Subtract the equations from each other to cancel out the 'x'.
(x - 2y = -16) - (x + 2y = 4)
= -4y = -20
-4y = -20
Divide by -4
y = 5
Now plug 5 in for y in the equations:
x - 2y = -16
x + 2y = 4
x - 10 = -16
x = -6
x + 10 = 4
x = -6
So , y = 5, and x = -6
3. 12x + 12y = 36
-8x - 8y = -8
Lets also simplify the equations.
(12x + 12y = 36) / 12 = x + y = 3
(-8x - 8y = -8) / -8 = x - y = 1
Right off the bat you can say that x = 2 and y = 1.
2 + 1 =3
2 - 1 = 1
But mathematically:
Subtract both equations
(x + y = 3) - (x - y = 1)
= 2y = 2
2y = 2
y = 1
x + 1 = 3
x = 2
x - 1 = 1
x = 2
So x = 2 and y = 1;
