Solve each system of linear equation and explain any method you used:
4x+1/3y=50
-3x-8y=-84
To solve the system of linear equations, we can use the method of substitution or the method of elimination.
Let's use the method of substitution to solve this system:
From the first equation, we can isolate "x" by subtracting 1/3y from both sides of the equation:
4x + (1/3)y = 50
4x = 50 - (1/3)y
x = (50 - (1/3)y)/4
Now we substitute this value of "x" into the second equation:
-3x - 8y = -84
-3((50 - (1/3)y)/4) - 8y = -84
Simplifying this equation step by step:
-3(50 - (1/3)y)/4 - 8y = -84
-3(50 - (1/3)y) - 32y = -336
-150 + (1/3)y - 32y = -336
-150 - 32y + (1/3)y = -336
(1/3)y - 32y = -336 + 150
-31(1/3)y = -186
-(4/3)y = -186
y = (-186)(-3/4)
y = 279/4
y = 69.75
Now we substitute the value of "y" back into the first equation to solve for "x":
4x + (1/3)(69.75) = 50
4x + 23.25 = 50
4x = 50 - 23.25
4x = 26.75
x = 26.75/4
x = 6.6875
Therefore, the solution to the system of equations is x = 6.6875 and y = 69.75.