Question 1102553: I need explanation how to solve this problem, thank you. I see some examples on the internet but there is no explanation how they get that result.
On the basis of data from 1990 to 2006, the median income y in year x for mean and women is approximated by the equations given below, where x=0 corresponds to 1990 and y is in constant 2006 dollars. If these equations remain valid in the future, when will with the median income of men and women be the same?
Men: -255x+2y=56,937
Women: - 842x+3y=42,751
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Both are linear equations. Where they intersect is where they are equal
-255x+2y=56,937
- 842x+3y=42,751
multiply top by -3 and bottom by 2 to eliminate y
765x-6y=-170811
-1684x+6y=85502 add them
-919x=-85309 divide by -919 both sides
x=92.83
substitute into first equation to get y
-23671.16+2y=56937
2y=80608.16
y=40304.08
Check in second equation
-842*92.83+3(40304.08)=42749.38, close enough with rounding.
x=92.83 which will be in 2073.83 or well into that year.
y=40304.08, which is what the income will be in constant 2006 dollars
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