How to solve by substitution: 8x - 4y = 16
y = 2x - 4
simplyfied
8x - 4y = 16
-2x + y = - 4
To solve the system of equations using substitution, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
In this case, equation 2 already gives us the value of y in terms of x: y = 2x - 4.
Step 2: Substitute the expression for the variable from step 1 into the other equation.
Substitute the value of y from equation 2 (which is 2x - 4) into equation 1:
8x - 4(2x - 4) = 16.
Step 3: Solve the resulting equation for the remaining variable.
Expand and simplify the equation:
8x - 8x + 16 = 16
16 = 16.
Step 4: Analyze the result.
Since the equation in step 3 is always true (16 = 16), it means that any value of x will satisfy the original system of equations. Therefore, the system has infinitely many solutions.
To summarize, the system of equations has infinitely many solutions.