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Question 343286: One number is 5 more than another number. If the smaller number is doubled and added to 3 times the larger number, the sum is 80. Find the two numbers.
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! x+5=y_2x+3y=80
Since 5 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 5 from both sides.
x=-5+y_2x+3y=80
Move all terms not containing x to the right-hand side of the equation.
x=y-5_2x+3y=80
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is y-5.
x=y-5_2(y-5)+3y=80
Multiply 2 by each term inside the parentheses.
x=y-5_2y-10+3y=80
Since 2y and 3y are like terms, add 3y to 2y to get 5y.
x=y-5_5y-10=80
Since -10 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 10 to both sides.
x=y-5_5y=10+80
Add 80 to 10 to get 90.
x=y-5_5y=90
Divide each term in the equation by 5.
x=y-5_(5y)/(5)=(90)/(5)
Simplify the left-hand side of the equation by canceling the common factors.
x=y-5_y=(90)/(5)
Simplify the right-hand side of the equation by simplifying each term.
x=y-5_y=18
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 18.
x=(18)-5_y=18
Remove the parentheses around the expression 18.
x=18-5_y=18
Subtract 5 from 18 to get 13.
x=13_y=18
This is the solution to the system of equations.
x=13_y=18
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