# SYSTEM OF EQUATIONS

May 28th, 2015
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1. Problem: Solve the following system:x + y = 11 3x - y = 5 Solution: Solve the first equation for y (you could solve for x - it doesn't matter) y = 11 - x Now, substitute 11 - x in the second equation.

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SYSTEM OF EQUATIONS1. Problem: Solve the following system: x + y = 11 3x - y = 5 Solution: Solve the first equation for y (you could solve for x - it doesn't matter). y = 11 - x Now, substitute 11 - x for y in the second equation. This gives the equation one variable, which earlier algebra work has taught you how to do. 3x - (11 - x) = 5 3x - 11 + x = 5 4x = 16 x = 4 Now, substitute 4 for x in either equation and solve for y. (We use the first equation below.) 4 + y = 11 y = 7 The solution is the ordered pair, (4, 7).The last method, addition, is probably the most complicated, but is necessary when dealing with more complex systems, such as systems with three or more variables. The idea behind the addition method is to replace an equation with a combination of the equations in the system. To obtain such a combination, you multiply each equation by a constant and add. You choose the constants so that the resulting coefficient of one of the variables will be 0. Example:2. Problem: Solve the following system: 5x + 3y = 7 3x - 5y = -23 Solution: Multiply the second equation by 5

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