Determine the number of solutions the system has. Then state whether the system of equations is consistent or inconsistent and if it is independent or dependent. y=−32x+5𝑦=-32𝑥+5 y=−23x+5
Question
Determine the number of solutions the system has. Then state whether the system of equations is consistent or inconsistent and if it is independent or dependent. y=−32x+5𝑦=-32𝑥+5 y=−23x+5
Solution
The system of equations given is:
- y = -32x + 5
- y = -23x + 5
To determine the number of solutions, we need to compare the coefficients of x and the constants in the two equations.
In both equations, the constant term is 5, but the coefficients of x are different (-32 in the first equation and -23 in the second equation). This means that the lines represented by these equations are parallel and do not intersect.
Therefore, the system of equations has no solutions.
A system of equations with no solutions is called inconsistent.
Since the equations represent parallel lines and do not coincide, they are independent.
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