Be able to use linear systems and reduced row echelon form to solve problems in different contexts where the linear system is not immediately apparent.
Build on our past work interpreting solutions to a linear system from the reduced row echelon form by further restricting to solutions which make sense in the context of a given problem.
Suppose we know that in a football game there were \(24\) points scored from \(8\) scoring occasions and also that the number of successful extra point kicks was equal to the number of successful two point conversions. Find all ways in which the points may have been scored in this game.
Pure elemental phosphorous and hypochlorous acid \(HClO\) react in water to make phosphoric acid \(H_3PO_4\) and hydrochloric acid \(HCl\text{.}\) Balance the chemical equation
You might know that two points determine a line. That’s because in a line \(y=mx+b\) there are two unknowns: the coefficient of the \(x\) term and the constant term. Note that in Reading Question 1 we needed three points to determine a specific quadratic function because there were three unknowns: the coefficient of the \(x^2\) term, the coefficient of the \(x\) term and the coefficient of the constant term.
Go through the same steps to attempt to find a quadratic function through the points \((0,0)\text{,}\)\((1,1)\text{,}\) and \((2,2)\text{.}\) What do you get, and why does the answer make sense?
In a basketball game, where points are scored either by a \(3\) point shot, a \(2\) point shot or a \(1\) point free throw, there were \(80\) points scored from \(30\) successful shots. Find all ways in which the points may have been scored in this game.
