SOLUTION: Jose bought a shirt and a sweater for a total of $65. The price of the sweater was $5 more than twice the price of the shirt. What was the price of the shirt?

Question 389072: Jose bought a shirt and a sweater for a total of $65. The price of the sweater was $5 more than twice the price of the shirt. What was the price of the shirt?
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
x+y=65_y=2x+5
Since y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting y from both sides.
x=-y+65_y=2x+5
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -y+65.
x=-y+65_y=2(-y+65)+5
Multiply 2 by each term inside the parentheses.
x=-y+65_y=-2y+130+5
Add 5 to 130 to get 135.
x=-y+65_y=-2y+135
Since -2y contains the variable to solve for, move it to the left-hand side of the equation by adding 2y to both sides.
x=-y+65_y+2y=135
Since y and 2y are like terms, add 2y to y to get 3y.
x=-y+65_3y=135
Divide each term in the equation by 3.
x=-y+65_(3y)/(3)=(135)/(3)
Simplify the left-hand side of the equation by canceling the common factors.
x=-y+65_y=(135)/(3)
Simplify the right-hand side of the equation by simplifying each term.
x=-y+65_y=45
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 45.
x=-(45)+65_y=45
Multiply -1 by the 45 inside the parentheses.
x=-45+65_y=45
Add 65 to -45 to get 20.
x=20_y=45
This is the solution to the system of equations.
x=20_y=45
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