How to Solve Linear Systems Using Addition

A linear system of equations is a system, or group, of equations in which the graph of each equation would be linear, or a straight line. By solving a linear system of equations you can determine where the equations intersect, or meet. One way to solve a linear system of equations to find their intersection, is by using the addition method.

Difficulty: Moderate

Instructions

Things You'll Need:

• Paper
• Pencil

1. Manipulate your equations so that both the x and the y variables are on the same side of both equations. Example: x=30-y and -5.7x=200-7.3y can be changed to x+y=30 and -5.7x+7.3y=200

2. Make the coefficients of one of the variables in each equation the opposite using multiplication Example: 5.7(x+y=30)=5.7x+5.7y=171 So, the x in one equation is 5.7 and in the other it is -5.7.

3. Add the two equations together. Example: (5.7x+5.7y=171)+(-5.7x+7.3y=200)=(13y=371) The coefficients of each x cancels the other x out so that we are left with only y.

4. Solve your new equation for the remaining variable. Example: 13y=371, y=28.538 after I divide both sides by 13.

5. Go back to one of your original equations and solve for the other variable. Example: -5.7x+7.3y=200 Plug in your new value for y. -5.7x+7.3(28.538)=200 Multiply out your new y value and its coefficient. -5.7x+208.331=200 Subtract 208.331 from each side of your equation. -5.7x=-8.331 Divide each side of the equation by -5.7, which leaves you with x=1.462 So, the final answer is (1.462, 28.538).

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