Final answer:
The value of x - 2y from the system of equations 3x + 2y = 48 and 2x + 3y = 12, is found to be 48 after solving the equations using the elimination method.
Step-by-step explanation:
The question at hand involves solving a set of two linear equations to find the value of x-2y. This is a standard problem of simultaneous equations that can be approached using methods such as substitution, elimination, or by means of matrices.
Given the equations:
To solve these equations, we can use the elimination method. We multiply the first equation by 2 and the second equation by 3 to align the coefficients of x and eliminate it:
Subtract the second equation from the first to eliminate x:
6x + 4y - (6x + 9y) = 96 - 36
Solving for y gives:
Substitute the value of y into the first equation:
3x + 2(-12) = 48
3x - 24 = 48
3x = 72
x = 24
Now, we need to find the value of x - 2y:
x - 2y = 24 - 2(-12) = 24 + 24 = 48
So, the value of x - 2y is 48.