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Questions and Answers
What is the primary purpose of Step 1 in the Substitution Method?
What is the primary purpose of Step 1 in the Substitution Method?
- To solve for x and y simultaneously
- To substitute the value of y in the other equation
- To find the value of one variable in terms of the other (correct)
- To reduce the equation to an equation in one variable
In the given example, what is the value of y obtained by solving the equation -29y = -19?
In the given example, what is the value of y obtained by solving the equation -29y = -19?
- y = 19/27
- y = 1/29
- y = 19/29 (correct)
- y = 29/19
What is the name of the method used to solve the pair of linear equations in the given example?
What is the name of the method used to solve the pair of linear equations in the given example?
- Algebraic Method
- Graphical Method
- Elimination Method
- Substitution Method (correct)
What happens if the statement obtained in Step 2 of the Substitution Method is true?
What happens if the statement obtained in Step 2 of the Substitution Method is true?
What is the value of x obtained by substituting y = 19/29 in Equation (3)?
What is the value of x obtained by substituting y = 19/29 in Equation (3)?
What is the purpose of Step 3 in the Substitution Method?
What is the purpose of Step 3 in the Substitution Method?
What is the name of the method that involves eliminating one variable to obtain an equation in the other variable?
What is the name of the method that involves eliminating one variable to obtain an equation in the other variable?
What happens if the statement obtained in Step 2 of the Substitution Method is false?
What happens if the statement obtained in Step 2 of the Substitution Method is false?
What is the purpose of Verification in solving systems of linear equations?
What is the purpose of Verification in solving systems of linear equations?
What is the name of the method that involves solving one equation for one variable and then substituting that expression into the other equation?
What is the name of the method that involves solving one equation for one variable and then substituting that expression into the other equation?
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.
