QQuestionMathematics
QuestionMathematics
Explain how to use the substitution method to solve a system of linear equations.
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Step 1:I'll explain how to solve a system of linear equations using the substitution method, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Substitution Method
The substitution method involves solving one equation for a variable and then substituting that expression into the other equation to solve for the remaining variable. This allows us to reduce a system of two equations to a single equation with one variable.
Step 3:: Select an Equation to Rearrange
x - y = 1
Choose one of the equations and solve it for one of the variables. Typically, select the equation that makes rearranging easier. Example System:
Step 4:: Solve for One Variable
From the first equation, solve for $$y$$:
y = 5 - 2x
Step 5:: Substitute the Expression
Substitute the expression for $$y$$ into the second equation:
x - (5 - 2x) = 1
Step 6:: Solve the Simplified Equation
x = 2
3x - 5 = 1
Step 7:: Back-Substitute to Find the Other Variable
y = 1
Using y = 5 - 2x:
Final Answer
Key Insights: - The substitution method works best when one equation can be easily rearranged - Always check your solution by substituting back into both original equations - This method reduces a two-variable problem to a single-variable equation
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