Systems of Equations

CONCEPTS

Methods of Solving Systems of Equations

• Substitution: 1) Solve 1 equation for 1 variable, 2) substitute that variable into the other equation, 3) solve

• Addition/Subtraction: If the coefficients of x or y are already opposite numbers, add the 2 equations to eliminate x or y

Infinite Solutions

• A set of equations can have infinite solutions when they are multiples of one another

EXAMPLE

• 5x + 4y = 10 & 10x + 8y = 20

PRACTICE PROBLEMS

Question 1 Let p & q be real numbers such that p + q = 4, -p * q = 12, and p > q. What is p?

-- Answer -- 6

q = 4 - p

-p (4 - p) = 12, p = 6

Question 2 For what values would the following equations demonstrate an infinite number of solutions?

x - 2y = 8

3x - 6y = 4a

-- Answer -- 6

4a = 8 * 3

a = 6

ACT PRACTICE PROBLEMS

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