Solve for xxx and yyy in the following pair of linear equations. 2x−5y=−32x−5y=−32x - 5y = -3 3x−6y=−43x−6y=−43x - 6y = -4

Question

Solve for xxx and yyy in the following pair of linear equations. 2x−5y=−32x−5y=−32x - 5y = -3 3x−6y=−43x−6y=−43x - 6y = -4

BlackTom AI · Accepted Answer

To solve the system, we need to evaluate each option against the two equations given.

Option a: x = 1, y = -1.
- Plug into the first equation: 2x − 5y = 2(1) − 5(−1) = 2 + 5 = 7, which does not equal −3. Therefore, this option is incorrect.

Option b: 'Other' indicates some alternate solution not listed. Since there are exactly two linear equations in two unknowns, there is a unique solution unless the system is inconsistent or dependent. We can test a concrete candidate from the other options to verify consistency; since option a fails, but we will evaluate the remaining numeric options to confirm.

Option c: x = −2/3, y = 1/3.
- Check the first equation: 2x − 5y = 2(−2/3) − 5(1/3) = (−4/3) − (5/3) = −9/3 = −3, which matches the right-hand side of the first equation.
- Check the second equation: 3x − 6y = 3(−2/3) − 6(1/3) = (−2) − (2) = −4, which matches the right-hand side of the second equation. This option satisfies both equations, so it is consistent.

Option d: x = 8, y = 1.
- First equation gives 2(8) − 5(1) = 16 − 5 = 11, not −3. Therefore, this option is incorrect.

Option e: x = 3, y = 5.
- First equation gives 2(3) − 5(5) = 6 − 25 = −19, not −3. Therefore, this option is incorrect.

Summarizing the checks: option a fails the first equation, option d fails the first equation, option e fails the first equation, option c satisfies both equations. The generic 'Other' option would be unnecessary since a valid numeric solution exists and is explicit in option c, making 'Other' an invalid choice in this context.

My LMS Subjects Maths for Biomedicine DECIMALS QUIZ

Solve for xxx and yyy in the following pair of linear equations. 2x−5y=−32x−5y=−32x - 5y = -3 3x−6y=−43x−6y=−43x - 6y = -4

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