Question
Solve the system of equations 6x+2y=-18 and 3x+y=24
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GPT 3.5
To solve the system of equations 6x + 2y = -18 and 3x + y = 24, we'll use the method of substitution.
First, let's solve one equation for one variable in terms of the other. In this case, we'll solve the second equation for y:
3x + y = 24
=> y = 24 - 3x
Now, we can substitute this expression for y into the first equation:
6x + 2(24 - 3x) = -18
=> 6x + 48 - 6x = -18
=> 48 = -18
Since this simplifies to a false statement, the system of equations is inconsistent. In other words, there is no solution that satisfies both equations simultaneously.
First, let's solve one equation for one variable in terms of the other. In this case, we'll solve the second equation for y:
3x + y = 24
=> y = 24 - 3x
Now, we can substitute this expression for y into the first equation:
6x + 2(24 - 3x) = -18
=> 6x + 48 - 6x = -18
=> 48 = -18
Since this simplifies to a false statement, the system of equations is inconsistent. In other words, there is no solution that satisfies both equations simultaneously.
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