12х + 9y = 18
-4x-3y=32
Elimation
To eliminate a variable, we need to multiply one or both of the equations by a constant so that the coefficient of one of the variables in one equation becomes the same as the coefficient of the same variable in the other equation.
Let's eliminate the variable "y":
Multiply the first equation by 3 and the second equation by 9 to make the coefficients of "y" the same:
3(12x + 9y) = 3(18)
9(−4x − 3y) = 9(32)
Simplifying:
36x + 27y = 54
-36x - 27y = 288
Now, sum the two equations:
(36x + 27y) + (-36x - 27y) = 54 + 288
0 = 342
The resulting equation, 0 = 342, is not true, which means there is no solution to the system of equations. Therefore, the system of equations is inconsistent.