Solve each system of linear equation and explain any method you used:
4x+1/3y=50
-3-8y=-84
To solve this system of linear equations:
Equation 1: 4x + (1/3)y = 50
Equation 2: -3 - 8y = -84
Method:
1. Let's start by isolating the y variable in Equation 2:
-3 - 8y = -84
Subtract -3 from both sides:
-8y = -81
Divide both sides by -8:
y = (-81)/(-8)
y = 10.125
2. Now that we have found the value of y, we can substitute it back into Equation 1 to solve for x:
4x + (1/3)y = 50
Substitute y = 10.125:
4x + (1/3)(10.125) = 50
Simplify:
4x + 3.375 = 50
Subtract 3.375 from both sides:
4x = 46.625
Divide both sides by 4:
x = 11.65625
Final solution:
x = 11.65625
y = 10.125
Therefore, the solution to the system of linear equations is x = 11.65625 and y = 10.125.