Is the system of equations consistent and independent, consistent and dependent, or inconsistent?

Question

y=−x+12y=−2x+2



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Answer 1

To determine if the system of equations is consistent and independent, consistent and dependent, or inconsistent, we can examine the two equations:

1. \( y = -x + 12 \)
2. \( y = -2x + 2 \)

We can analyze the slopes and intercepts of the lines represented by these equations.

1. The first equation \( y = -x + 12 \) has a slope of \(-1\) and a y-intercept of \(12\).
2. The second equation \( y = -2x + 2 \) has a slope of \(-2\) and a y-intercept of \(2\).

Since the slopes of the two lines are different (\(-1\) and \(-2\)), the lines intersect at exactly one point. Therefore, the system of equations has a unique solution.

Thus, the system of equations is:

Consistent and independent.