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Find the number of solutions to each system 2x - y + 4 = 0 and 4x - 2y + 8 = 0
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GPT 3.5
To find the number of solutions to the system of equations, we can use the method of elimination. We want to eliminate one variable, so that we can solve for the other.
First, we can multiply the first equation by 2:
2(2x - y + 4) = 2(0)
4x - 2y + 8 = 0
Notice that this equation is the same as the second equation in the system. This means that the two equations represent the same line, and there are infinitely many solutions to the system.
In other words, every point on the line 4x - 2y + 8 = 0 is a solution to the system.
First, we can multiply the first equation by 2:
2(2x - y + 4) = 2(0)
4x - 2y + 8 = 0
Notice that this equation is the same as the second equation in the system. This means that the two equations represent the same line, and there are infinitely many solutions to the system.
In other words, every point on the line 4x - 2y + 8 = 0 is a solution to the system.