Can anyone help me to understand algebra? Right now I am working on Systems of Linear Equations
in Two Variables and I do not understand any of it. Thank you.
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Of course! I'd be happy to help you understand algebra, specifically systems of linear equations in two variables. Here's a step-by-step explanation of how to approach solving these types of problems:
1. Understand the concept: A system of linear equations in two variables involves finding the values of two variables that satisfy both equations simultaneously. The goal is to find the values that make both equations true.
2. Identify the variables: Start by identifying the variables in the system. Typically, they are represented by x and y.
3. Write the equations: Write down the two linear equations that make up the system. Each equation will have both x and y variables, along with constants. For example, the equations might be:
Equation 1: 3x + 2y = 7
Equation 2: 2x - y = 4
4. Choose a method for solving: There are different methods to solve systems of linear equations, such as the graphing method, substitution method, and elimination method. We'll cover the elimination method here.
5. Elimination method: Using the elimination method, the goal is to eliminate one of the variables by multiplying one or both equations by a suitable constant so that the coefficients of one variable in both equations are opposite or the same.
6. Add or subtract the equations: Add or subtract the two equations in order to eliminate one variable. The objective is to reduce the system to one equation with only one variable. In our example, we can multiply Equation 2 by 2 to make the coefficients of x in both equations the same:
(2)(2x - y) = (2)(4) becomes 4x - 2y = 8
7. Solve for the remaining variable: Solve the resulting equation for the remaining variable. In this case, solve for x. We now have the equation:
3x + 2y = 7
4x - 2y = 8
8. Solve for x: Add the two equations together to eliminate y:
(3x + 2y) + (4x - 2y) = 7 + 8
7x = 15
Divide both sides by 7 to solve for x:
x = 15/7 (or simplify further if possible)
9. Substitute x back into an equation: Substitute the value of x into either equation to solve for y. Let's use Equation 1:
3x + 2y = 7
3(15/7) + 2y = 7
10. Solve for y: Simplify the equation and solve for y:
45/7 + 2y = 7
2y = 7 - 45/7
Then, solve for y.
11. Check: Finally, check your solution by substituting the values of x and y into both original equations to ensure they satisfy both equations.
I hope this step-by-step guide helps you understand how to solve systems of linear equations in two variables. If you have any further questions, feel free to ask!