Final answer:
To solve a system of equations algebraically using either substitution or elimination, first identify the system of equations. Then, choose the appropriate method and manipulate the equations to eliminate one variable. Solve for the remaining variable and substitute the value back into the original equations to find the other variable.
Step-by-step explanation:
When solving a system of equations algebraically using either substitution or elimination, step one is to identify the system of equations that needs to be solved. Let's say we have the following system of equations:
Equation 1: 2x + 3y = 6
Equation 2: 4x - 2y = 8
Step two involves determining which method, substitution or elimination, to use. In this case, we can choose elimination.
Step three is to manipulate the equations in order to eliminate one variable. We can do this by multiplying Equation 1 by 2 and Equation 2 by 3, resulting in:
Equation 1: 4x + 6y = 12
Equation 2: 12x - 6y = 24
By adding Equation 1 and Equation 2 together, the y variable is eliminated and we are left with:
16x = 36
Step four requires solving for the remaining variable. Dividing both sides of the equation by 16 gives us:
x = 2.25
Step five is to substitute the value of x back into one of the original equations to solve for the other variable. Using Equation 1:
2(2.25) + 3y = 6
4.5 + 3y = 6
3y = 1.5
y = 0.5
We have now solved the system of equations algebraically using elimination, and the solution is x = 2.25 and y = 0.5.