Can we use the modified equation to find the value of the variable in solving simultaneous equations? If no is there any exception?

Write the fraction or mixed number and the decimal shown by the model

Mason and christian go to the movie theater and purchase refreshments for their friends. mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks. christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks. write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. using these equations, determine and state the price of a drink, to the nearest cent.

What is the missing justification in the proof of the pythagorean identity below, sin^2x+cos^2x=1, using a right triangle?