Final answer:
To solve the system of equations, we used the elimination method to find y = -54, then substituted this value back into one of the original equations to solve for x, resulting in x = 50.
Step-by-step explanation:
To solve the system of linear equations algebraically, we'll employ methods such as substitution or elimination to find the values of x and y that satisfy both equations simultaneously. In this case, we have the system:
4x + 3y = 38
12x + 5y = 330
First, let's use the elimination method to eliminate one of the variables. In this case, we can multiply the first equation by 3 and the second equation by -1 to eliminate y:
(3)(4x) + (3)(3y) = (3)(38) yields 12x + 9y = 114
(-1)(12x) + (-1)(5y) = (-1)(330) yields -12x - 5y = -330
Adding both equations, we get 12x + 9y - 12x - 5y = 114 - 330, which simplifies to 4y = -216. Dividing both sides by 4, we find y = -54.
Next, we substitute y = -54 into one of the original equations, for instance, into 4x + 3y = 38:
4x + 3(-54) = 38
4x - 162 = 38
4x = 200
x = 50
The solution to the system of equations is x = 50 and y = -54.