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Solving simultaneous equations -elimination Using the same equations from above, we will illustrate how to solve for x and y using the method of elimination. (1) (2) In the method of elimination, we examine both equations and see if it is possible to eliminate a variable by either adding or subtracting like terms. 1 Arrange the linear equation such that one of the two unknowns becomes the subject of the equation. x + 2y = 1 x = 2 Substitute the new equation from step 1 into the non-linear equation. Simplify and express in the form ax2 + bx + c = 0. ()2 + 4y2 = 13 = 0 3 Solve the quadratic equation by factorisation, completing the square or by using the. Mathematics Learning Centre, University of Sydney 3 Solving simultaneous equations by the elimination method Suppose we have a pair of simultaneous equations, 2x? y = ?2 and x+y = 5. We can solve these equations by taking the sum of the left hand sides and equating it to the sum of the right hand sides as follows: 2x?y +(x+y)=3x =3.

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