Solve the pair of simultaneous equations; (1) y + 4x + 1 = 0, (2) y^2 + 5x^2 + 2x = 0 .

Rearrage equation (1) to make y the subject of the formula. This gives y = -4x -1 .

Substitute this value of y into equation (2). This gives (-4x -1)^2 +5x^2 +2x = 0 . 

Expanding out the brackets gives 16x^2 + 8x + 1 + 5x^2 +2x =0 .

Collecting all the like terms gives 21x^2 +10x + 1 = 0 .

Factorising this equation gives (7x + 1)(3x + 1) = 0 which means x = -1/7, -1/3 . 

Substituting these x values back into (1) implies that y = - 3/7, 1/3 .