 Welcome to solving systems of linear equations using the addition or subtraction method. In this activity, we will find the common solution of two or more linear equations in two variables. The equations in this type of problem are referred to as a system of linear equations or as simultaneous linear equations. A solution to a system of equations is the ordered pair or pairs that satisfy all equations in the system. Follow these steps to solve a system of equations using the addition or subtraction method. 1. If necessary, rewrite the equations so that the variables appear on one side of the equal sign and constants on the other. 2. If necessary, multiply one or both equations by a constant or constants so that when you add or subtract the equations, the result will be an equation with only one variable. 3. Add or subtract the equations to obtain an equation in one variable. 4. Solve the equation for the variable. 5. Substitute the value found in step 4 into either of the original equations and solve for the other variable. Example 1. Eliminating a variable by the addition method. Add the two equations together. Then solve for the remaining variable to get x equals 5. Substitute 5 for x in either of the original equations and solve for y. The solution to this system is 5, 3. Example 2. Eliminating a variable by the subtraction method. Subtract the equations. Solve for the remaining variable to get y equals 5. Substitute 5 for y in either of the original equations and solve for x to get x equals negative 8. The solution to this system is negative 8 and 5. Example 3. Multiplying one equation using the addition method. Multiply the first equation by 3, which gives us 6x minus 3y equals 21. Add the equations and solve for x. Substitute 3 for x in either of the original equations and solve for y to get y equals negative 1. The solution to this system is 3 and negative 1. Example 4. Multiplying both equations using the subtraction method. Multiply the first equation by 3. Multiply the second equation by 2. Add the equations to get y equals 3. Substitute 3 for y in either of the original equations and solve for x to get x equals negative 2. The solution to this system is negative 2 and 3. Now it's your turn. Use the addition method to find a solution to the following system of linear equations. Add the equations. Solve for x. Substitute and solve for the other variable. The solution to this system is 2 and 1. Use the subtraction method to find a solution to the following system of linear equations. Subtract the equations to get x equals 2. Substitute and solve for the other variable to get y equals 1. The solution to this system is 2 and 1. Multiply one of the equations by a constant. Multiply the bottom equation by what number? You could use 2 or 3. We will use 3 to get rid of the y terms. This gives 6x minus 3y equals 12. Move the top equation under this and add the equations. Solve for the remaining variable. Substitute and solve for the other variable. The solution to the system is 1.5 and negative 1. Note, a dependent system of equations is one in which no unique solution can be determined. Multiplying this bottom equation by negative 2 gives 2x minus 6y equals 16. Since the lines are the same, the coordinates at any point on the lines represent a solution. Note, an inconsistent system of equations is one in which there is no solution. Multiply this bottom equation by 2. Then subtract. Since we know 0 does not equal negative 1, we conclude that there is no solution. Try to solve the next 10 systems of equations. We will show one method to solve each system as well as the correct solution. Please pause the video while you solve each system. Congratulations! You've completed solving systems of linear equations using the addition or subtraction method.