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: \(x\) = hours Eleanor works at Job A, \(y\) = hours Eleanor works at Job B. |
| None | The sum of three numbers is 24 . The third is 7 m… | Let's denote the three numbers as \(x\), \(y\), and \(z\). |
| 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 \(y = 3x\). We can substitute this into the equation \(4x + 3y = 39\) to solve fo… |
| None | Solve the system of equations. $-10 x+3 y=5 ; x=y… | The system of equations is given as $-10 x+3 y=5$ and $x=y-4$. The goal is to find the values of x … |
| None | Solve the following system of equations with the … | First, we solve the first equation for x: \(x = -3y - 1\) |
| 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: \[\begin{array}{r} x+y=-12 \\ y=-4 x \end{array}\] |
| None | Solve the following system by the substitution me… | First, we can express \(x\) in terms of \(y\) from the first equation: \(x = 3 - y\). |
| None | Solve the system of equations by the substitution… | The system of equations is given by: \(x = 3y + 3\) and \(x = 8y - 7\). |
| 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… |