To solve the system, one can either manipulate equations to eliminate variables or isolate one variable then substitute its expression into other equations, leading to a two-variable system.
Step-by-step explanation:
To solve the system of equations algebraically and reduce it to a two-variable system with variables r and l, one can employ two different methods. The first method requires us to manipulate the equations of bouquet A and bouquet C. We multiply the equation for bouquet A by an appropriate factor so that when it is added to the equation for bouquet C, we eliminate one variable and reduce the system to two variables. Similarly, we do the same with bouquet B and bouquet C.
The second method involves isolating one variable in the equation for bouquet B by using algebraic operations such as subtraction and division. Once one variable is expressed in terms of the other, it can be substituted into the equations for bouquets A and C to find the values for r and l. This approach transforms a three-variable system into a two-variable one.
Both methods involve careful algebraic steps such as multiplication, addition, subtraction, division, and substitution to solve for the remaining variables once one variable is eliminated or isolated.
The probable question can be: Consider two ways to algebraically solve the system of equations representing this situation. Complete the statements describing how to solve the system by reducing it to a two-variable system with r and /. Select the correct response from each drop-down. First method: Multiply the equation for bouquet A by □ , and add it to the equation for bouquet C. Then multiply the equation for bouquet B by , and add it to the equation for bouquet C. Second method: Rewrite the equation for bouquet B by subtracting from both sides of the equation. Then divide both sides by , and substitute the expression for in the equations for bouquets A and C.