A student bought a calculator and a textbook for a course in algebra. He told his friend that the total cost was $115 without tax and that the calculator cost $10 more than twice the cost of the textbook. What was the cost of each item. Let x= the cost of a calculator and y= the cost of the text book the corresponding modeling system is x+y=115. X=2y+10 solve the system by using the method of substitution. Enter the ordered pair
To solve the system of equations by substitution, we can start by solving one of the equations for one of the variables and then substituting that expression into the other equation.
From the first equation, we have x + y = 115. We can solve this equation for x by subtracting y from both sides:
x = 115 - y
Now, we can substitute this expression for x into the second equation, which is x = 2y + 10:
115 - y = 2y + 10
Next, we can simplify and solve for y:
115 - 10 = 2y + y
105 = 3y
y = 35
Now that we have the value of y, we can substitute it back into either of the original equations to find the value of x. Let's use the first equation:
x + 35 = 115
x = 115 - 35
x = 80
Therefore, the cost of the calculator is $80 and the cost of the textbook is $35. The ordered pair representing this is (80, 35).