solve the following system by the substitution method 1/2x + 2/3y =-31/2 3x-y=12
To solve the system of equations by the substitution method, we can isolate one variable in terms of the other from one equation and substitute it into the other equation.
From the first equation, 1/2x + 2/3y = -31/2, we can isolate x:
1/2x = -31/2 - 2/3y
x = (-31/2)(2/1) - (2/3)(2/1)y
x = -31 - (4/3)y
x = -31 - (4/3)y
Now we can substitute this expression for x into the second equation, 3x - y = 12:
3(-31 - (4/3)y) - y = 12
-93 - 4y - y = 12
-5y - 93 = 12
-5y = 12 + 93
-5y = 105
y = 105 / -5
y = -21
Now that we have found the value of y, we can substitute it back into the expression for x to find its value:
x = -31 - (4/3)(-21)
x = -31 + (4/3)(21)
x = -31 + (4/3)(7)(3)
x = -31 + (4)(7)
x = -31 + 28
x = -3
Therefore, the solution to the system of equations is x = -3 and y = -21.