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If 2x + y = 13 and 4x – y = 17, find the value of (x – y). solve this with substitute method?
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If 2x + y = 13 and 4x – y = 17, find the value of (x – y). solve this ...
To solve the system of equations using the substitution method, follow these detailed steps:
Step 1: Write down the equations
- The given equations are:
- 1) 2x + y = 13
- 2) 4x – y = 17
Step 2: Solve one equation for one variable
- From equation 1 (2x + y = 13), we can express y in terms of x:
- y = 13 - 2x
Step 3: Substitute into the second equation
- Now, substitute the expression for y into equation 2 (4x – y = 17):
- 4x - (13 - 2x) = 17
Step 4: Simplify and solve for x
- Distribute the negative sign:
- 4x - 13 + 2x = 17
- Combine like terms:
- 6x - 13 = 17
- Add 13 to both sides:
- 6x = 30
- Divide by 6 to solve for x:
- x = 5
Step 5: Substitute back to find y
- Substitute x = 5 back into the expression for y:
- y = 13 - 2(5)
- y = 13 - 10
- y = 3
Step 6: Find the value of (x - y)
- Now, calculate (x - y):
- x - y = 5 - 3
- x - y = 2
Final Answer
- The value of (x - y) is 2.
Step 1: Write down the equations
- The given equations are:
- 1) 2x + y = 13
- 2) 4x – y = 17
Step 2: Solve one equation for one variable
- From equation 1 (2x + y = 13), we can express y in terms of x:
- y = 13 - 2x
Step 3: Substitute into the second equation
- Now, substitute the expression for y into equation 2 (4x – y = 17):
- 4x - (13 - 2x) = 17
Step 4: Simplify and solve for x
- Distribute the negative sign:
- 4x - 13 + 2x = 17
- Combine like terms:
- 6x - 13 = 17
- Add 13 to both sides:
- 6x = 30
- Divide by 6 to solve for x:
- x = 5
Step 5: Substitute back to find y
- Substitute x = 5 back into the expression for y:
- y = 13 - 2(5)
- y = 13 - 10
- y = 3
Step 6: Find the value of (x - y)
- Now, calculate (x - y):
- x - y = 5 - 3
- x - y = 2
Final Answer
- The value of (x - y) is 2.
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If 2x + y = 13 and 4x – y = 17, find the value of (x – y). solve this with substitute method?
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If 2x + y = 13 and 4x – y = 17, find the value of (x – y). solve this with substitute method? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If 2x + y = 13 and 4x – y = 17, find the value of (x – y). solve this with substitute method? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2x + y = 13 and 4x – y = 17, find the value of (x – y). solve this with substitute method?.
If 2x + y = 13 and 4x – y = 17, find the value of (x – y). solve this with substitute method? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If 2x + y = 13 and 4x – y = 17, find the value of (x – y). solve this with substitute method? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2x + y = 13 and 4x – y = 17, find the value of (x – y). solve this with substitute method?.
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