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Questions and Answers
What is the primary purpose of Step 1 in the Substitution Method?
In the given example, what is the value of y obtained by solving the equation -29y = -19?
What is the name of the method used to solve the pair of linear equations in the given example?
What happens if the statement obtained in Step 2 of the Substitution Method is true?
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What is the value of x obtained by substituting y = 19/29 in Equation (3)?
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What is the purpose of Step 3 in the Substitution Method?
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What is the name of the method that involves eliminating one variable to obtain an equation in the other variable?
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What happens if the statement obtained in Step 2 of the Substitution Method is false?
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What is the purpose of Verification in solving systems of linear equations?
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What is the name of the method that involves solving one equation for one variable and then substituting that expression into the other equation?
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Study Notes
Algebraic Methods of Solving a Pair of Linear Equations
- The graphical method is not convenient when the point representing the solution of the linear equations has non-integral coordinates.
Substitution Method
- Solve a pair of linear equations by substitution method.
- Steps to solve:
- Step 1: Write one variable in terms of the other from one of the equations.
- Step 2: Substitute the value of the variable in the other equation to eliminate one variable.
- Step 3: Solve the equation in one variable to get its value.
- Step 4: Substitute the value of the variable in either of the original equations to get the value of the other variable.
Example 4: Substitution Method
- Solve the pair of equations: 7x – 15y = 2, x + 2y = 3.
- Substitute x = 3 – 2y in the first equation to eliminate x.
- Solve the equation in one variable to get the value of y, then substitute back to get the value of x.
Elimination Method
- Multiply both equations to make the coefficients of one variable equal, then subtract one equation from the other to eliminate the variable.
Example 9: Elimination Method
- Solve the pair of equations: 2x + 3y = 8, 4x + 6y = 7.
- Multiply the first equation by 2 and the second equation by 1 to make the coefficients of x equal.
- Subtract the second equation from the first to eliminate x, resulting in a false statement, implying no solution.
Example 10: Word Problem
- A two-digit number and the number obtained by reversing the digits sum up to 66, and the digits differ by 2.
- Let the tens and units digits in the first number be x and y, respectively.
- Solve the equations to find the value of x and y.
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Description
Learn about solving a pair of linear equations graphically, its limitations and alternative algebraic methods in this math quiz.
