x - 2y = 1 , x^2 + y^2 = 13 find the solutions to this quadratic equation
equation 1) x - 2y = 1equation 2) x2 + y2 = 13
Rearrange equation 1 to: x = 1+2ysubstitute into equation 2: (1+2y)2 + y2=13expand first bracket: (1+2y)(1+2y) +y2 =13(1+4y+4y2) +y2 = 13Collect like terms: 5y2+4y-12=0Factorise by recognition: (5y-6)(y+2)=0solve each bracket: y= 6/5 or y=-2Rearrange equation 1: x= 1+2ySubstitute y values into equation 1: x= 1+ 2(6/5) = 17/5x= 1+2(-2)= -3
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