How to solve a linear equation in two variables?
There are several methods to solve a linear equation in two variables. One common method is the substitution method. Here's a step-by-step guide on how to solve a linear equation in two variables using the substitution method:
- Step 1: Write down the given equation
Start by writing down the linear equation in two variables. For example, let's say we have the equation 2x + 3y = 10.
- Step 2: Solve for one variable
Choose one variable to solve for in terms of the other variable. For example, if we choose to solve for x, we can rearrange the equation to get x in terms of y: x = (10 - 3y) / 2.
- Step 3: Substitute the expression
Substitute the expression for x back into the original equation. In our example, we would substitute (10 - 3y) / 2 for x in the equation 2x + 3y = 10.
- Step 4: Solve for the remaining variable
Now that we have an equation with only one variable, solve for that variable. In our example, we would solve for y by simplifying the equation obtained in the previous step.
- Step 5: Find the value of the other variable
Once you have found the value of one variable, substitute it back into one of the original equations to find the value of the other variable. In our example, we would substitute the value of y back into x = (10 - 3y) / 2 to find the value of x.
By following these steps, you can solve a linear equation in two variables using the substitution method.