-w-z=-2 and 4w+5z=16 im trying to solve this equation by using subsitution
To solve the system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable.
Let's solve the first equation, -w - z = -2, for w.
-w - z = -2
-w = z - 2
w = -z + 2
Step 2: Substitute the expression for the variable you solved for into the other equation.
Substitute (-z + 2) for w in the second equation, 4w + 5z = 16:
4(-z + 2) + 5z = 16
-4z + 8 + 5z = 16
z + 8 = 16
z = 16 - 8
z = 8
Step 3: Substitute the value of z back into one of the original equations to solve for the remaining variable.
Let's use the first equation, -w - z = -2:
-w - 8 = -2
-w = -2 + 8
-w = 6
w = -6
Step 4: Check your solution by substituting the values of w and z into both original equations.
Substituting w = -6 and z = 8 into the first equation (-w - z = -2):
-(-6) - 8 = -2
6 - 8 = -2
-2 = -2 (True)
Substituting w = -6 and z = 8 into the second equation (4w + 5z = 16):
4(-6) + 5(8) = 16
-24 + 40 = 16
16 = 16 (True)
Both equations are satisfied, and the solution is w = -6 and z = 8.