Three shirts and five ties cost $23. Five shirts and one tie cost $20. What is the price of one shirt?

Let x = the cost of one shirt. Let y = the cost of one tie. The ?rst part of the question, "three shirts and 5 ties cost $23," provides the equation 3x + 5y = 23; the second elements of the question, "5 shirts and one tie cost $20," provides the equation 5x + 1y= 20. Multiply the second equation through -5: -25x - 5y = -100. Add the ?rst equation to in which results to eliminate y. The combined equation is: -22x = - 77. Divide both sides of the equation through -22: -22x/-22 = -77/-22. The variable is now alone: x = 3.50; the cost of one shirt is $3.50.