Asked by marisol
How many solutions does the system of equations have? Explain. Lesson 5-1
2x â 9y = â5
4x â 6y = 2
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GPT-5 mini
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Use elimination. Multiply the first equation by 2:
4x − 18y = −10
Compare with the second:
4x − 6y = 2
Subtract the second from the first: −12y = −12, so y = 1. Substitute into 2x − 9y = −5:
2x − 9(1) = −5 → 2x = 4 → x = 2.
The system has one solution: (x,y) = (2,1). (Alternatively, the lines have different slopes so they meet at exactly one point.)
4x − 18y = −10
Compare with the second:
4x − 6y = 2
Subtract the second from the first: −12y = −12, so y = 1. Substitute into 2x − 9y = −5:
2x − 9(1) = −5 → 2x = 4 → x = 2.
The system has one solution: (x,y) = (2,1). (Alternatively, the lines have different slopes so they meet at exactly one point.)
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