3.2 Solving Systems Algebraically When you try to solve a system of equations by graphing, the coordinates of the point of intersection may not be obvious.

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Presentation transcript:

3.2 Solving Systems Algebraically When you try to solve a system of equations by graphing, the coordinates of the point of intersection may not be obvious. You can solve a system of equations by writing equivalent systems until the value of one variable is clear. Then substitute to find the value(s) of the other variable(s). You can use the substitution method to solve a system of equations when it is easy to isolate one of the variables. – After isolating the variable, substitute for that variable in the other equation. Then solve for the other variable.

Solving by Substitution What is the solution of the system of equations? 3x + 4y = 12 2x + y = 10 The solution is (5.6, -1.2).

Solving by Elimination What is the solution of the system of equations? 4x + 2y = 9 -4x + 3y = 16

Equivalent Systems When you multiply each side of one or both equations in a system by the same nonzero number, the new system and the original system have the same solutions. The two systems are called equivalent systems. You can use this method to make additive inverses.

Solving an Equivalent System What is the solution of the system of equations? 2x + 7y = 4 3x + 5y = -5 2x + 7y = 4  6x + 21y = 12 3x + 5y = -5  -6x – 10y = 10 11y = 22 y = 2 2x + 7(2) = 4 2x + 14 = 4 x = -5 The solution is (-5, 2).

More Practice!!!!! Homework – Textbook p. 146 # 10 – 18, 22 – 42.