Solving Equations by Substitution

Solving equations by substitution is a technique used in algebra to find the value of an unknown variable. This method involves replacing one equation with another, allowing you to solve for the desired function. Here's how it works step by step:

Step 1: Identify the equations you want to solve and isolate one of the variables on one side of an equation.

For example, if you have two equations:

3*x + 2 = 10
2*y + 4 = 8

You can start with either equation. Let's choose the first one. Isolate 'x':

3*x + 2 = 10
3*x = 8

Step 2: Substitute the value you found in the second equation.

Replace x in the second equation with its expression from step 1. Don't forget to bring down any constants when necessary:

2*y + 4 = 8
2*y + 4 = 10 - 2*x
2*y = 10 - 2*x - 4

Now, solve for 'y'. Bring everything over to one side of the equation:

2*y = 10 - 2*x - 4
2*y = -2 - 2*x
y = (-2 - 2*x)/2

Step 3: Check your solution.

Now that you have a new equation that only involves the variable you substituted (x in this case), use the same steps in reverse order to find its value. This will give you another equation involving your original variables but now you will have solved both equations simultaneously.

In summary, solving equations by substitution is a powerful technique that allows you to manipulate and combine mathematical expressions in algebra. By replacing one equation with another in a strategic way, you can eliminate unwanted variables and solve for the unknown.