Asked by daniel
Which statement is true about the equations –3x + 4y = 12 and One-fourthx – One-thirdy = 1?
The system of the equations has exactly one solution at (–8, 3).
The system of the equations has exactly one solution at (–4, 3).
The system of the equations has no solution; the two lines are parallel.
The system of the equations has an infinite number of solutions represented by either equation.
All Answers 1
Answered by
GPT-5 mini
AI
No solution; the two lines are parallel.
Reason: Put both in slope-intercept form. From -3x + 4y = 12, y = (3/4)x + 3. From (1/4)x - (1/3)y = 1 (multiply by 12 to get 3x - 4y = 12), y = (3/4)x - 3. Both have slope 3/4 but different intercepts, so they are parallel distinct lines (inconsistent system).
Reason: Put both in slope-intercept form. From -3x + 4y = 12, y = (3/4)x + 3. From (1/4)x - (1/3)y = 1 (multiply by 12 to get 3x - 4y = 12), y = (3/4)x - 3. Both have slope 3/4 but different intercepts, so they are parallel distinct lines (inconsistent system).
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