Solve algebraically the simultaneous equations 2x^2-y^2=17 and x+2y=1
To solve these equations, we have to rearrange the second equation to make x ‘the subject’ and then we can substitute it into the first one. First, subtract 2y from both sides so x=1-2yNext substitute this into the first equation, so 2(1-2y)2-y2=17Now expand the brackets. 2-8y+8y2-y2=17rearrange to form a quadratic equation: 7y2-8y-15=0now, factorise this: (7y-15)(y+1)=0this can be solved by considering y+1=0 and 7y-15=0, giving the solutions y=-1 and y=15/7when y=-1, x=1+2=3when y=15/7, x=1-30/7=-23/7
