The method of substitution is an algebraic technique used for discovering precise solutions for a system of equations. It requires the resolution of one equation for a single variable, followed by the replacement of this derived expression into the other equation. This process effectively removes one variable, facilitating the solution for the remaining one.
| Topic | Problem | Solution |
|---|---|---|
| None | Consider the following word problem: Eleanor is w… | Let's denote: |
| None | The sum of three numbers is 24 . The third is 7 m… | Let's denote the three numbers as |
| None | Solving a percent mixture problem using a linear … | Let's denote the number of panels produced by Plant B as x. The total number of defective panels is… |
| None | Solving a word problem with two unknowns using a … | Let's denote the cost of the bench as x and the cost of the garden table as y. |
| None | Use the substitution property of equations to sol… | We are given that |
| None | Solve the system of equations. $-10 x+3 y=5 ; x=y… | The system of equations is given as |
| None | Solve the following system of equations with the … | First, we solve the first equation for x: |
| None | Find the solutions to the system of nonlinear equ… | The system of equations is nonlinear because one of the equations is quadratic. To find the solutio… |
| None | A small publishing company is planning to publish… | A small publishing company is planning to publish a new book. The production costs will include one… |
| None | Solve the system by the substitution method. \[ \… | The system of equations can be solved by substitution method. Here, the second equation is already … |
| None | Solve the system by the substitution method. \[ \… | The system of equations is given as: |
| None | Solve the following system by the substitution me… | First, we can express |
| None | Solve the system of equations by the substitution… | The system of equations is given by: |
| None | Jolene invests her savings in two bank accounts, … | Let's denote the amount of money Jolene invested at 9 percent as x. Then, the amount of money she i… |