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An introduction to systems of linear equations in two variables, explaining the concepts of inconsistent and non-unique solutions. It presents two methods for solving such systems: the substitution method and the elimination method. Examples and explanations for each method.
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Solving A System of Linear Equations Graphically :
The Substitution Method :
y m x b y m x b
x x x x x x
And y = 2( 1)โ โ 1 = โ 3 Solution: (โ1, โ3) Check: 2( 1)โ โ โ( 3) = 1, ( 1)โ + 2( 3)โ = โ 7_._ Yes
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The Elimination Method :
a y b x c a y b x c
x y x y y y
3 x + 4(1) = โ2, โ 3 x โ 5(1) = 1 โ x = โ 2 (Note that using both is a way to check) The solution is (โ2, 1)
x y x y y
3 x + 4(3) = 6 or 2 x + 3(3) = 5 โ x = โ 2 (Note that using both is a way to check) The solution is (โ2, 3)
What Can Go Wrong?
x y x y
No ( x , y ) satisfy the system (no solution)