Simultaneous Equations – eliminating fractions

Question 6 Solve the simultaneous equations y  4  3x and

y2 2 x. x

Solution Rearrange and label equation 1 y  4  3x

y  3x  4  1 Multiply each term by x Label equation  2  y2 2 x x y2  x  2  x  x x y  2  2 x  x2  2 Substitute 1 into  2 

 y   2  2 x  x2  3x  4   2  2 x  x 2

Simplify 3x  6  2 x  x 2 x2  x  6  0 Factorize, solve for x Find the corresponding value of y  x  3  x  2   0

x30 x3 From 1 , y  3x  4  3  3  4 5

or x20 x  2 From 1 , y  3x  4  3  2   4  10 Answer statement   x, y    3,5 ,  2, 10 

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