SOLUTION: the difference between two numbers is 21 and their sum is 185.find the largest number

Question 391287: the difference between two numbers is 21 and their sum is 185.find the largest number
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
x-y=21_x+y=185
Since -y does not contain the variable to solve for, move it to the right-hand side of the equation by adding y to both sides.
x=y+21_x+y=185
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is y+21.
x=y+21_(y+21)+y=185
Remove the parentheses around the expression y+21.
x=y+21_y+21+y=185
Since y and y are like terms, add y to y to get 2y.
x=y+21_2y+21=185
Since 21 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 21 from both sides.
x=y+21_2y=-21+185
Add 185 to -21 to get 164.
x=y+21_2y=164
Divide each term in the equation by 2.
x=y+21_(2y)/(2)=(164)/(2)
Simplify the left-hand side of the equation by canceling the common factors.
x=y+21_y=(164)/(2)
Simplify the right-hand side of the equation by simplifying each term.
x=y+21_y=82
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 82.
x=(82)+21_y=82
Remove the parentheses around the expression 82.
x=82+21_y=82
Add 21 to 82 to get 103.
x=103_y=82
This is the solution to the system of equations.
x=103_y=82
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