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Definitions A system of linear equations is two or more linear equations whose solution we are trying to find. (1) y = 4 x – 6 (2) y = – 2 x A solution to a system of equations is the ordered pair or pairs that satisfy all equations in the system. The solution to the above system is (1, – 2).
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Solutions Determine if ( – 4, 16) is a solution to the system of equations. y = – 4 x y = – 2 x + 8 (1) y = – 4 x 16 = – 4( – 4) 16 = 16 (2) y = – 2 x + 8 16 = – 2( – 4) + 8 16 = 8 + 8 16 = 16 Yes, it is a solution Example:
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Solutions Determine if ( – 2, 3) is a solution to the system of equations. x + 2 y = 4 y = 3 x + 3 (1) x + 2 y = 4 – 2 + 2(3) = 4 – 2 + 6 = 4 4 = 4 (2) y = 3 x + 3 3 = 3( – 2) + 3 3 = – 6 + 3 3 = – 3 But… Example: So it is NOT a solution
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