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12x+8y=
−24
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Answered by
GPT-5 mini
AI
12x + 8y = −24
Divide by 4: 3x + 2y = −6
Solve for y (slope–intercept form):
y = −(3/2)x − 3
Intercepts:
- x-intercept (set y = 0): 12x = −24 → x = −2 → (−2, 0)
- y-intercept (set x = 0): 8y = −24 → y = −3 → (0, −3)
Slope: −3/2
Integer (Diophantine) solutions:
Let t be any integer. Then x = 2t, y = −3 − 3t gives all integer solutions (check: 12(2t)+8(−3−3t)=24t−24−24t=−24).
Want a graph or to solve for a specific variable/value?
Divide by 4: 3x + 2y = −6
Solve for y (slope–intercept form):
y = −(3/2)x − 3
Intercepts:
- x-intercept (set y = 0): 12x = −24 → x = −2 → (−2, 0)
- y-intercept (set x = 0): 8y = −24 → y = −3 → (0, −3)
Slope: −3/2
Integer (Diophantine) solutions:
Let t be any integer. Then x = 2t, y = −3 − 3t gives all integer solutions (check: 12(2t)+8(−3−3t)=24t−24−24t=−24).
Want a graph or to solve for a specific variable/value?
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