![]() ![]() ![]() To review how to solve equations, check out our post: Solving One-Step Equations. So, we can easily substitute that value for x into the other equation and solve for y. Let’s look at the system of linear equations below:įirst, notice we are given the value of one of the variables, x. Solving systems algebraically involves manipulating the equations we are given to uncover the values of each of the variables.īut when must a system of linear equations be solved algebraically? When solving systems of equations, we should generally choose the method that takes the least effort and leaves the least room for error. There are multiple methods for solving systems of equations, including solving systems algebraically. Solving Systems of Equations Algebraically What about situations where we have two or more variables and two or more equations? These systems of equations can seem more challenging, but solving systems of linear equations by substitution is often the easiest way to find solutions. The equation above has only one variable. There is an algebraic property of equality called the Substitution Property, which states: If x=y, then x may be replaced by y in expressions and equations.įor example, we can substitute 7 for x in the following equation. In the study of Algebra, we learn how to substitute variables for mathematical values in expressions. In each of these examples of substitution, we are replacing one entity with another equivalent one to solve a problem or reach a goal. Finally, when we run into construction on our drive home and take a different road, we’re substituting one route for another. Next, we can substitute vegan alternatives to animal products in a recipe. First, when the pitcher on a softball team hurts her shoulder, another player can take her place as a substitute. To understand solving systems of equations by substitution, let’s first think about what substitution means.
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