Solve each system of linear equation and explain any method you used:
4x+1/3y=50
-3x-8y=-84
To solve this system of linear equations, we will use the method of elimination.
First, we want to eliminate one variable so that we can solve for the other variable. To eliminate the x variable, we need to create equal coefficients for x in both equations. To do this, we will multiply the first equation by 3 and the second equation by 4:
(3)*(4x + (1/3)y) = (3)*50
(4)*(-3x - 8y) = (4)*(-84)
This simplifies the equations to:
12x + y = 150
-12x - 32y = -336
Now, we will add the two equations together to eliminate the x variable:
(12x + y) + (-12x - 32y) = 150 + (-336)
-31y = -186
(Note: The x terms cancel out)
Dividing both sides of the equation by -31 gives us:
y = 6
Now that we have found the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
4x + (1/3)(6) = 50
4x + 2 = 50
4x = 48
x = 12
Therefore, the solution to the system of linear equations is x = 12 and y = 6.