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Solve the following pair of linear equations by the substitution method. 0. 2x + 0. 3y = 1. 3 and 0. 6x + 0. 5y = 2. 3?
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Solve the following pair of linear equations by the substitution metho...
Substitution Method for Solving Linear Equations
- Given Equations:
- 2x + 0.3y = 1.3
- 0.6x + 0.5y = 2.3
Step 1: Solve one equation for one variable
- Let's solve the first equation for x:
- 2x + 0.3y = 1.3
- 2x = 1.3 - 0.3y
- x = (1.3 - 0.3y)/2
Step 2: Substitute the value of x into the second equation
- Substitute x = (1.3 - 0.3y)/2 into the second equation:
- 0.6((1.3 - 0.3y)/2) + 0.5y = 2.3
- 0.6(1.3 - 0.3y) + 0.5y = 2.3
- 0.78 - 0.18y + 0.5y = 2.3
Step 3: Solve for y
- Simplify the equation:
- 0.78 + 0.32y = 2.3
- 0.32y = 2.3 - 0.78
- 0.32y = 1.52
- y = 1.52/0.32
- y = 4.75
Step 4: Substitute the value of y back into the first equation
- Use y = 4.75 in the first equation:
- 2x + 0.3(4.75) = 1.3
- 2x + 1.425 = 1.3
- 2x = 1.3 - 1.425
- 2x = -0.125
- x = -0.125/2
- x = -0.0625
Step 5: Check the solution
- Substitute x = -0.0625 and y = 4.75 into both original equations to ensure they satisfy both equations.
Therefore, the solution to the given pair of linear equations is x = -0.0625 and y = 4.75.
- Given Equations:
- 2x + 0.3y = 1.3
- 0.6x + 0.5y = 2.3
Step 1: Solve one equation for one variable
- Let's solve the first equation for x:
- 2x + 0.3y = 1.3
- 2x = 1.3 - 0.3y
- x = (1.3 - 0.3y)/2
Step 2: Substitute the value of x into the second equation
- Substitute x = (1.3 - 0.3y)/2 into the second equation:
- 0.6((1.3 - 0.3y)/2) + 0.5y = 2.3
- 0.6(1.3 - 0.3y) + 0.5y = 2.3
- 0.78 - 0.18y + 0.5y = 2.3
Step 3: Solve for y
- Simplify the equation:
- 0.78 + 0.32y = 2.3
- 0.32y = 2.3 - 0.78
- 0.32y = 1.52
- y = 1.52/0.32
- y = 4.75
Step 4: Substitute the value of y back into the first equation
- Use y = 4.75 in the first equation:
- 2x + 0.3(4.75) = 1.3
- 2x + 1.425 = 1.3
- 2x = 1.3 - 1.425
- 2x = -0.125
- x = -0.125/2
- x = -0.0625
Step 5: Check the solution
- Substitute x = -0.0625 and y = 4.75 into both original equations to ensure they satisfy both equations.
Therefore, the solution to the given pair of linear equations is x = -0.0625 and y = 4.75.
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Solve the following pair of linear equations by the substitution method. 0. 2x + 0. 3y = 1. 3 and 0. 6x + 0. 5y = 2. 3? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Solve the following pair of linear equations by the substitution method. 0. 2x + 0. 3y = 1. 3 and 0. 6x + 0. 5y = 2. 3? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following pair of linear equations by the substitution method. 0. 2x + 0. 3y = 1. 3 and 0. 6x + 0. 5y = 2. 3?.
Solve the following pair of linear equations by the substitution method. 0. 2x + 0. 3y = 1. 3 and 0. 6x + 0. 5y = 2. 3? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Solve the following pair of linear equations by the substitution method. 0. 2x + 0. 3y = 1. 3 and 0. 6x + 0. 5y = 2. 3? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following pair of linear equations by the substitution method. 0. 2x + 0. 3y = 1. 3 and 0. 6x + 0. 5y = 2. 3?.
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