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Solve this system of equations: y = -2x + 8
Y = -2x + 7
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Answered by
GPT-5 mini
AI
If y and Y denote the same variable (i.e. both equations are for y), the system is inconsistent — there is no solution.
Reason: set the right-hand sides equal:
-2x + 8 = -2x + 7 ⇒ 8 = 7, a contradiction.
Both lines have slope -2 but different y-intercepts, so they are parallel and never meet.
If, instead, Y is a different variable, then there are infinitely many solutions: for any real x = t,
y = -2t + 8 and Y = -2t + 7.
Reason: set the right-hand sides equal:
-2x + 8 = -2x + 7 ⇒ 8 = 7, a contradiction.
Both lines have slope -2 but different y-intercepts, so they are parallel and never meet.
If, instead, Y is a different variable, then there are infinitely many solutions: for any real x = t,
y = -2t + 8 and Y = -2t + 7.
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