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Solve the linear equation by eliminating 'x'(substitution method) -x+ 3y=8 ; 4x 7y=25?
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Solve the linear equation by eliminating 'x'(substitution method) -x+...
Substitution Method to Solve Linear Equations
The substitution method is a way to solve a system of linear equations by substituting one equation into the other and solving for one variable.
Given Equations:
- x - 3y = 8
- 4x + 7y = 25
Step 1: Solve for x in one of the equations
- x - 3y = 8
- x = 8 + 3y
Step 2: Substitute the value of x from Step 1 into the other equation
- 4x + 7y = 25
- 4(8 + 3y) + 7y = 25
Step 3: Simplify and solve for y
- 32 + 12y + 7y = 25
- 19y = -7
- y = -7/19
Step 4: Substitute the value of y into the equation from Step 1 to solve for x
- x = 8 + 3y
- x = 8 + 3(-7/19)
- x = 209/19
Step 5: Check the solution
- Substitute the values of x and y into both equations to check if they are true.
- (-209/19) - 3(-7/19) = 8
- 4(-209/19) + 7(-7/19) = 25
Final Answer:
- x = 209/19, y = -7/19
The substitution method is a way to solve a system of linear equations by substituting one equation into the other and solving for one variable.
Given Equations:
- x - 3y = 8
- 4x + 7y = 25
Step 1: Solve for x in one of the equations
- x - 3y = 8
- x = 8 + 3y
Step 2: Substitute the value of x from Step 1 into the other equation
- 4x + 7y = 25
- 4(8 + 3y) + 7y = 25
Step 3: Simplify and solve for y
- 32 + 12y + 7y = 25
- 19y = -7
- y = -7/19
Step 4: Substitute the value of y into the equation from Step 1 to solve for x
- x = 8 + 3y
- x = 8 + 3(-7/19)
- x = 209/19
Step 5: Check the solution
- Substitute the values of x and y into both equations to check if they are true.
- (-209/19) - 3(-7/19) = 8
- 4(-209/19) + 7(-7/19) = 25
Final Answer:
- x = 209/19, y = -7/19
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Solve the linear equation by eliminating 'x'(substitution method) -x+ 3y=8 ; 4x 7y=25? 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 linear equation by eliminating 'x'(substitution method) -x+ 3y=8 ; 4x 7y=25? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the linear equation by eliminating 'x'(substitution method) -x+ 3y=8 ; 4x 7y=25?.
Solve the linear equation by eliminating 'x'(substitution method) -x+ 3y=8 ; 4x 7y=25? 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 linear equation by eliminating 'x'(substitution method) -x+ 3y=8 ; 4x 7y=25? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the linear equation by eliminating 'x'(substitution method) -x+ 3y=8 ; 4x 7y=25?.
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