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2x − 3y = −14
3x − 2y = −6
If (x, y) is a solution to the system of equations above, what is the value of x − y ?
3x − 2y = −6
If (x, y) is a solution to the system of equations above, what is the value of x − y ?
- a)−20
- b)−8
- c)−4
- d)8
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
2x − 3y = −143x − 2y = −6If (x, y) is a soluti...
Choice C is correct. Multiplying each side of the equation 2x − 3y = −14 by 3 gives 6x − 9y = −42.
Multiplying each side of the equation 3x − 2y = −6 by 2 gives 6x − 4y = −12.
Then, subtracting the sides of 6x − 4y = −12 from the corresponding sides of 6x − 9y = −42 gives −5y = −30.
Dividing each side of the equation −5y = −30 by −5 gives y = 6.
Finally, substituting 6 for y in 2x − 3y = −14 gives 2x − 3(6) = −14, or x = 2.
Therefore, the value of x − y is 2 − 6 = −4.
Alternatively, adding the corresponding sides of 2x − 3y = −14 and 3x − 2y = −6 gives 5x − 5y = −20, from which it follows that x − y = −4.
Choices A, B, and D are incorrect and may be the result of an arithmetic error when solving the system of equations.
Multiplying each side of the equation 3x − 2y = −6 by 2 gives 6x − 4y = −12.
Then, subtracting the sides of 6x − 4y = −12 from the corresponding sides of 6x − 9y = −42 gives −5y = −30.
Dividing each side of the equation −5y = −30 by −5 gives y = 6.
Finally, substituting 6 for y in 2x − 3y = −14 gives 2x − 3(6) = −14, or x = 2.
Therefore, the value of x − y is 2 − 6 = −4.
Alternatively, adding the corresponding sides of 2x − 3y = −14 and 3x − 2y = −6 gives 5x − 5y = −20, from which it follows that x − y = −4.
Choices A, B, and D are incorrect and may be the result of an arithmetic error when solving the system of equations.
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2x − 3y = −143x − 2y = −6If (x, y) is a soluti...
The expression 2x means 2 times x.
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2x − 3y = −143x − 2y = −6If (x, y) is a solution to the system of equations above, what is the value of x − y ?a)−20b)−8c)−4d)8Correct answer is option 'C'. Can you explain this answer?
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