Question

Solve the simultaneous equations
y = 4x + 1
y = 2x^2+ 7x - 1

Answer 1

`Given,\\y = 4x+1......(1)\\y = 2x^2+7x-1.............(2)\\Equating~equation (1)~and~(2),\\4x+1 = 2x^(2) +7x-1\\or, 2x^(2)+7x-4x-1-1=0\\or, 2x^(2) + 3x-2=0\\or, 2x^(2) +4x-x-2=0\\or, 2x(x+2)-1(x+2)=0\\or, (x+2)(2x-1)=0\\i.e. x=-2 ~or~ (1)/(2) \\When~x=2,~equation(1)~becomes ~y=4(-2) +1=-7\\When~x=-(1)/(2),~equation (1)~becomes~y=4((1)/(2)) +1 = 2+1=3`

So, the required values of x are -2 and 1/2 and that of y are -7 and 3.