Podcast
Questions and Answers
What is the primary goal when solving a system of equations?
What is the primary goal when solving a system of equations?
- To find the values of the variables that satisfy both equations (correct)
- To identify the coefficients of the equations
- To determine if the equations are linear
- To rewrite the equations in standard form
Which method involves replacing one variable with an expression from another equation?
Which method involves replacing one variable with an expression from another equation?
- Addition
- Elimination
- Isolation
- Substitution (correct)
In the equation $2x + y = 10$, isolating y leads to which of the following?
In the equation $2x + y = 10$, isolating y leads to which of the following?
- y = 10 + 2x
- y = 10 - 2x (correct)
- y = 2x - 10
- y = -2x + 10
What is the first step when using substitution to solve the system of equations?
What is the first step when using substitution to solve the system of equations?
After substituting $x = 6 - y$ into the equation $2x + y = 10$, what is the resulting equation?
After substituting $x = 6 - y$ into the equation $2x + y = 10$, what is the resulting equation?
What should be done after obtaining the equation $-2y + y = -2$?
What should be done after obtaining the equation $-2y + y = -2$?
How does one eliminate a variable when using the elimination method?
How does one eliminate a variable when using the elimination method?
When isolating the variable y in the expression $12 - 2y + y = 10$, what should be the next step?
When isolating the variable y in the expression $12 - 2y + y = 10$, what should be the next step?
Flashcards
System of Equations
System of Equations
Two or more equations with the same variables, needing to find values that make all equations true.
Substitution Method
Substitution Method
Replacing one variable from one equation into another, to solve for other variables.
Isolate a Variable
Isolate a Variable
Get a variable alone on one side of an equation.
Elimination Method
Elimination Method
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Parentheses Multiplication
Parentheses Multiplication
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Combine Like Terms
Combine Like Terms
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Solving for a variable
Solving for a variable
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Example: x + y = 6. x =
Example: x + y = 6. x =
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Study Notes
Solving Systems of Equations
- A system of equations comprises two or more equations with the same variables (like x or y).
- The goal is to find the values of the variables that satisfy all the equations.
- Systems of equations can be represented as 3x - 2y = 6 and x + y = -8.
Methods for Solving Systems
- Substitution: In this method, one variable is replaced with an expression from another equation to solve a second equation.
Example using Substitution
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Given equations:
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x + y = 6
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2x + y = 10
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Isolate a variable: x = 6 - y from the first equation.
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Substitute: Plug in (6 - y) for x in the second equation: 2(6 - y) + y = 10
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Simplify: 12 - 2y + y = 10
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Solve for y: -y = -2, therefore y = 2
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Substitute back for x: x + 2 = 6; x = 4
Conclusion
- The solution is x = 4, y = 2
- The steps for solving systems of equations are essential to find accurate solutions
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Description
This quiz covers the methods for solving systems of equations, particularly focusing on the substitution method. You will learn how to isolate variables and substitute them into other equations to find solutions. Get ready to practice with provided examples!
