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Question 343480: The question is: You can find the years of Napoleon's birth and death by solving the following system: 3x-2y=1665 and -4x+3y=-1613. Napoleon crossed the Alps in 1797. How old was he when he crossed the Alps?
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! 3x-2y=1665_-4x+3y=-1613
Since -2y does not contain the variable to solve for, move it to the right-hand side of the equation by adding 2y to both sides.
3x=2y+1665_-4x+3y=-1613
Divide each term in the equation by 3.
(3x)/(3)=(2y)/(3)+(1665)/(3)_-4x+3y=-1613
Simplify the left-hand side of the equation by canceling the common factors.
x=(2y)/(3)+(1665)/(3)_-4x+3y=-1613
Combine the numerators of all expressions that have common denominators.
x=(2y+1665)/(3)_-4x+3y=-1613
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is ((2y+1665))/(3).
x=(2y+1665)/(3)_-4((2y+1665)/(3))+3y=-1613
Remove the parentheses around the expression 2y+1665.
x=(2y+1665)/(3)_-4((2y+1665)/(3))+3y=-1613
Divide each term in the numerator by the denominator.
x=(2y)/(3)+(1665)/(3)_-4((2y+1665)/(3))+3y=-1613
Reduce the expression (1665)/(3) by removing a factor of 3 from the numerator and denominator.
x=(2y)/(3)+555_-4((2y+1665)/(3))+3y=-1613
Remove the parentheses around the expression 2y+1665.
x=(2y)/(3)+555_-4((2y+1665)/(3))+3y=-1613
Divide each term in the numerator by the denominator.
x=(2y)/(3)+555_-4((2y)/(3)+(1665)/(3))+3y=-1613
Reduce the expression (1665)/(3) by removing a factor of 3 from the numerator and denominator.
x=(2y)/(3)+555_-4((2y)/(3)+555)+3y=-1613
Multiply -4 by each term inside the parentheses.
x=(2y)/(3)+555_-(8y)/(3)-2220+3y=-1613
Find the LCD (least common denominator) of -(8y)/(3)+3y+607.
x=(2y)/(3)+555_Least common denominator: 3
Multiply each term in the equation by 3 in order to remove all the denominators from the equation.
x=(2y)/(3)+555_-(8y)/(3)*3+3y*3=607*3
Simplify the left-hand side of the equation by canceling the common factors.
x=(2y)/(3)+555_y=607*3
Multiply 607 by 3 to get 1821.
x=(2y)/(3)+555_y=1821
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 1821.
x=(2(1821))/(3)+555_y=1821
Multiply 2 by 1821 in the numerator.
x=(2*1821)/(3)+555_y=1821
Multiply 2 by 1821 to get 3642.
x=(3642)/(3)+555_y=1821
Reduce the expression (3642)/(3) by removing a factor of 3 from the numerator and denominator.
x=1214+555_y=1821
Add 555 to 1214 to get 1769.
x=1769_y=1821
This is the solution to the system of equations.
x=1769_
y=1821
If he crossed the Alps in 1797 and was born in 1769, he was 28 years old.
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