Questions: On the basis of data from the years 2000 through 2015, seasonally adjusted median weekly earnings y in year x for men and women in a given area can be approximated by the following equations, where x=0 corresponds to the year 2000 and y is in current dollars. If these equations remain valid in the future, will earnings for women catch up with men within the next decade? Women: -783 x+50 y=24,950 Men: -88 x+5 y=3,200 Choose the correct answer below. A. Yes. The equations intersect at a positive x-value, which is after the year 2015. This indicates that the earnings for men and women will be the same in the next decade. B. No. The equations intersect at a negative x-value, which is before the year 2000. However, since the equations are linear, they cannot share another intersection point. This indicates that the earnings for men and women will not be the same in the next decade. C. Yes. The equations indicate that the earnings for men and

On the basis of data from the years 2000 through 2015, seasonally adjusted median weekly earnings y in year x for men and women in a given area can be approximated by the following equations, where x=0 corresponds to the year 2000 and y is in current dollars. If these equations remain valid in the future, will earnings for women catch up with men within the next decade? Women: -783 x+50 y=24,950 Men: -88 x+5 y=3,200 Choose the correct answer below. A. Yes. The equations intersect at a positive x-value, which is after the year 2015. This indicates that the earnings for men and women will be the same in the next decade. B. No. The equations intersect at a negative x-value, which is before the year 2000. However, since the equations are linear, they cannot share another intersection point. This indicates that the earnings for men and women will not be the same in the next decade. C. Yes. The equations indicate that the earnings for men and
Transcript text: On the basis of data from the years 2000 through 2015, seasonally adjusted median weekly earnings $y$ in year $x$ for men and women in a given area can be approximated by the following equations, where $x=0$ corresponds to the year 2000 and $y$ is in current dollars. If these equations remain valid in the future, will earnings for women catch up with men within the next decade? Women: $\quad-783 x+50 y=24,950$ Men: \[ -88 x+5 y=3,200 \] Choose the correct answer below. A. Yes. The equations intersect at a positive $x$-value, which is after the year 2015. This indicates that the earnings for men and women will be the same in the next decade. B. No. The equations intersect at a negative $x$-value, which is before the year 2000. However, since the equations are linear, they cannot share another intersection point. This indicates that the earnings for men and women will not be the same in the next decade. C. Yes. The equations indicate that the earnings for men and
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Solution

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Solution Steps

Step 1: Solve the system of linear equations

To find the intersection point, we solve the system of equations:

  1. $-783x + 50y = 24950$

  2. $-88x + 5y = 3200$

Using the determinant method, we calculate the determinant $D = a_1b_2 - a_2b_1$.

Substituting the given values, $D = -783_5 + 88_50 = 485$.

Since $D \neq 0$, the system has a unique solution. We find $x$ and $y$ as follows:

$x = \frac{Dx}{D} = \frac{-35250}{485} = -72.68$

$y = \frac{Dy}{D} = \frac{-310000}{485} = -639.18$

Step 2: Check if the x value of the intersection point falls within the desired timeframe

The intersection point at $x = -72.68$ does not fall within the desired timeframe from year 15 to 25.

Final Answer:

The earnings for the two groups will not be the same within the specified timeframe.

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