The Addition/Elimination Method serves as an effective tool in solving systems of linear equations. This technique revolves around the concept of adding or subtracting the equations with an aim to eliminate one of the variables. This subsequently allows for the resolution of the remaining variable. This method is particularly efficient in determining the point of intersection between two lines.
| Topic | Problem | Solution |
|---|---|---|
| None | Solve for the variable x in the system of equatio… | We are given the system of equations: \(\begin{array}{l}4 x+z=4 \ x-y+4 z=-11 \ -3 x+y-5 z=11\end{a… |
| None | Solve the following system of equations using the… | Multiply the second equation by 2 to get \(6x + 2y = 8\) |
| None | A variable needs to be eliminated to solve the sy… | The system of equations is already set up in a way that makes it easy to eliminate x. If we add the… |
| None | Solve by elimination. \[ \begin{array}{r} x-y=-4 … | We are given the system of equations: \[\begin{array}{r} x-y=-4 \\ 2x+4y=16 \end{array}\] |
| None | Solve for the value of x in the system of equatio… | We are given the system of equations: \(6x + y - z = 4\), \(2x + 3y + 5z = 20\), and \(-x + 2y - 4z… |
| None | A party rental company has chairs and tables for … | Represent the problem with the following equations: \(4c + 8t = 89\) and \(2c + 3t = 34\), where c … |
| None | sYstems Solving a value mixture problem using a s… | Translate the problem into a system of linear equations. Let's denote the time the Foster family's … |
| None | Solving a value mixture problem using a system of… | Let's denote the rate of the first mechanic as x and the rate of the second mechanic as y. Then we … |
| None | Paul has two jobs, working at a restaurant and tu… | Paul earns $14 an hour at the restaurant and has already worked 5 hours. So, he has already earned … |
| None | \[ \begin{array}{l} 4 x-2 y=7 \\ 7 x+2 y=15 \end{… | The system of equations is given by: \[\begin{array}{l} 4x - 2y = 7 \\ 7x + 2y = 15 \end{array}\] |
| None | Suppose that $-x+y=9$ and $2 x+3 y=17$. What is $… | We have a system of two linear equations: \(-x + y = 9\) and \(2x + 3y = 17\). |
| None | Suppose that $x+y=2$ and $2 x+y=6$. What is $x$ ?… | We have a system of two linear equations: \(x + y = 2\) and \(2x + y = 6\). |
| None | An investment of $\$ 92,000$ was made by a busine… | Let's denote the amounts of the three parts of the investment as x, y, and z for the first, second,… |
| None | Solve the system with the addition method: \[ \le… | Given the system of equations: \[\left\{\begin{array}{l} 5x+2y=-4 \\ -6x-5y=3 \end{array}\right.\] |
| None | Solve by Elimination/Addition \[ \left\{\begin{ar… | The given system of equations is: \[\left\{\begin{array}{l} 3 x+6 y=-6 \\ 9 x+18 y=-18 \end{array}\… |
| None | Solve the system by elimination. \[ \left\{\begin… | The system of equations is given as: \[\left\{\begin{array}{l} x+y=4 \\ -x-3 y=-6 \end{array}\righ… |
| None | Use a system of linear equations in three variabl… | The problem involves three variables, x, y, and z, which represent the number of packages of 6, 12,… |
| None | Find the solution to the system of equations: \[ … | We are given a system of linear equations with three variables as follows: |
| None | Solve the system with the addition method: \[ \le… | Add the two equations together to eliminate the variable x: -6x + 9y + 6x + 8y = 81 + 4, which simp… |
| None | Use a system of linear equations with two variabl… | Let's denote the number of student tickets as x and the number of adult tickets as y. We then have … |
| None | Maricopa's Success scholarship fund receives a gi… | Let's denote the amount invested in CDs as x, the amount invested in bonds as x + 15000, and the am… |
| None | The admission fee at an amusement park is $\$ 3.7… | Let's denote the number of children as x and the number of adults as y. We know that the total numb… |
| None | A 6000 -seat theater has tickets for sale at $\$ … | Let's denote the number of tickets sold at $28 as x and the number of tickets sold at $40 as y. We … |
| None | Ned, the owner of Ned's Nut Shop, sells peanuts f… | Ned, the owner of Ned's Nut Shop, sells peanuts for $10 per pound and cashews for $9 per pound. He … |
| None | Solve the given system of equations. \[ \begin{ar… | First, we represent the system of equations in matrix form. The matrix A is \[\begin{bmatrix} 5 & 4… |
| None | 9. Milk and cream contain different percents of b… | Let's denote the volume of the 3% milk as x (in liters) and the volume of the 15% cream as y (in li… |
| None | $\left\{\begin{array}{l}x-2 y+z=1 \\ y+2 z=-9 \\ … | Given the system of linear equations: \(\begin{cases} x-2y+z=1 \\ y+2z=-9 \\ x+y+3z=-14 \end{cases}… |
| None | The sum of three numbers is 10. The sum of twice … | We have a system of three equations that we can solve using linear algebra. The equations are: \(x … |
| None | Solve the given system of equations. \[ \begin{ar… | Represent the system of equations in matrix form as follows: \[\begin{bmatrix} 3 & 5 & -3 \\ 2 & -5… |
| None | Orange juice, a raisin bagel, and a cup of coffee… | Let's denote the cost of orange juice, a raisin bagel, and a cup of coffee before the increase as O… |
| None | $\left\{\begin{array}{l}2 x-y=3 \\ \frac{x-y}{2}+… | Este é um sistema de equações lineares. Podemos resolvê-lo pelo método de substituição ou eliminaçã… |
| None | b) $\left\{\begin{array}{l}x-y=3 \\ x+2 y=9\end{a… | Esta é uma sistema de equações lineares. Podemos resolvê-lo por substituição ou eliminação. Vou usa… |
| None | $\left\{\begin{array}{l}4 x-y=8 \\ x+y=7\end{arra… | \(\begin{cases} 4x-y=8 \\ x+y=7 \end{cases}\) |
| None | $\left\{\begin{array}{l}x+2 y=6 \\ 3 x-y=4\end{ar… | \(\left\{\begin{array}{l}x+2 y=6 \\ 3 x-y=4\end{array}\right.\) |
| None | Solve the system by the elimination/addition meth… | \(\begin{array}{l} 3x+2y=10 \\ -4x-3y=-13 \end{array}\) |
| None | $\begin{array}{l}\frac{1}{2} x-\frac{2}{3} y=6 \\… | \(\frac{1}{2}x - \frac{2}{3}y = 6\) and \(\frac{1}{4}x + \frac{1}{3}y = -1\) |
| None | $\left\{\begin{array}{l}3 x+2 y=5 \\ -3 x+4 y=1\e… | \(\begin{cases} 3x + 2y = 5 \\ -3x + 4y = 1 \end{cases}\) |
| None | $\left\{\begin{array}{l}2 x+y=9 \\ x=6 y-2\end{ar… | \(\left\{\begin{array}{l}2 x+y=9 \\ x=6 y-2\end{array}\right.\) |
| None | Three times one number added to another number is… | Let the first number be x and the second number be y. The given equations are: |
| None | 5a) \[ \begin{array}{l} x+y=3 \\ x-y=7 \end{array… | \(\begin{array}{l} x+y=3 \\ x-y=7 \end{array}\) |
| None | $\left\{\begin{array}{l}x+y=5 \\ x+150 y=9\end{ar… | \(\left\{\begin{array}{l}x+y=5 \\ x+150 y=9\end{array}\right.\) |
| None | E. $\quad x \geq 0$ Question 7 The solution of th… | Multiply the first equation by 3 and the second equation by 2 to make the coefficients of y equal: |
| None | 9. A preschool playground has both bicycles and t… | Let the number of bicycles be x and the number of tricycles be y. We have two equations: |
| None | 1. $\left\{\begin{array}{l}2 x+y=-10 \\ x-3 y=2\e… | Multiply the first equation by 3 and the second equation by 1 to make the coefficients of y equal: … |
| None | The solution to the simultaneous equations \[ 5 x… | Multiply the first equation by 3 and the second equation by 5 to make the coefficients of y equal: … |
| None | $\mathrm{ExOO}^{3}$ \[ \left\{\begin{array}{l} a^… | Solve the second equation for a: \(a = b + 10\) |
| None | $\begin{array}{l}3 x+2 y=-18 \\ 2 x+9 y=-12\end{a… | Multiply the first equation by 2 and the second equation by 3: \(\begin{cases} 6x + 4y = -36 \\ 6x … |
| None | ra Calculator - MathPapa \( \times \mid+ \) Is-of… | \( \frac{1}{8} (8x - 4y) = \frac{1}{8} (16) \) |
| None | Solve: \( \left\{\begin{array}{l}2 x^{2}-6 y^{2}=… | \( x^{2} = 51 - 3y^{2} \) |
| None | Solve the following system of equations. \[ \begi… | \(x = 3y + 17\) |
| None | Find the solution of the system of equations. \[ … | Step 1: Solve the second equation for \(x\): \[x = \frac{-5y - 46}{3}\] |
| None | \( \left\{\begin{array}{l}x+y=175 \\ x=4 y+20\end… | 1. Substitute x from equation 2 into equation 1: \(y+4y+20=175\) |
| None | Let \( \boldsymbol{x} \) be the time during the f… | \( x + y = 5 \) |
| None | Find the solution of the system of equations. \[ … | \( \begin{cases} 5x = 5y + 10 \\ 6x = 1 - 5y \end{cases} \) |
| None | Find the solution of the system of equations. \[ … | \(1^{st}\) equation \(-9x + 8y = -26\) |
| None | Part 2 of 2 Points: 0.5 of 1 Swimming Pool On a c… | Let x be the number of children and y be the number of adults. |
| None | \( \left\{\begin{array}{l}3 x-2 y=4 \\ 2 x+3 y=7\… | Add the two equations together to eliminate y: |