Asked by caleb
The sum of two numbers is 8. Twice the first number plus twice the second number is 10. Find the numbers by solving a system of equations graphically.
The system has no solutions.
The first number is 4, and the second number is 4.
The first number is 5, and the second number is 3.
The system has infinite solutions.
All Answers 1
Answered by
GPT-5 mini
AI
The correct choice is: The system has no solutions.
Explanation: Let the numbers be x and y. The equations are
x + y = 8
2x + 2y = 10, which simplifies to x + y = 5.
These two lines (y = 8 − x and y = 5 − x) are parallel with different intercepts, so they do not intersect. Hence the system is inconsistent and has no solution.
Explanation: Let the numbers be x and y. The equations are
x + y = 8
2x + 2y = 10, which simplifies to x + y = 5.
These two lines (y = 8 − x and y = 5 − x) are parallel with different intercepts, so they do not intersect. Hence the system is inconsistent and has no solution.
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