Find the solutions to the simultaneous equations

y - 2x = 3 x² + y² = 18Step 1- re-arrange the first formula to find y: y = 3 + 2x Step 2- Substitution: x² + ( 3 + 2x )² = 18 Step 3- Expand the brackets: ( 3 + 2x )( 3 + 2x ) = 9 + 6x + 6x + 4x² x² + 9 + 12x + 4x² = 18 5x² + 12x + 9 = 18 Step 4- Make the equation equal to zero and factorise: 5x² + 12x - 9 = 0 ( 5x - 3 ) ( x + 3 ) = 0 Step 5- Solve for x: x = -3 or 3/5 Step 6- Substitute the x values into the original equation to find y: y - 2x = 3 y - 2 ( -3 ) = 3 y + 6 = 3 y = -3 or, y - 2 ( 3/5 ) = 3 y - 6/5 = 3 y = 4 1/5 Answer: x = -3 or 3/5 and y = -3 or 4 1/5