Solve the equations y = x + 1 and y = x^2 - 3x + 4 simultaneously.
The first step is to identify that the first equation is linear and the second equation is a quadratic as indicated by the x squared term. Next, take the first linear equation and substitute for y in the second equation: x + 1 = x2 - 3x + 4.Rearrange the equation by bringing the terms on the left hand side over to the right hand side and grouping like terms: 0 = x2 - 3x - x + 4 - 1.Simplify the equation: x2 - 4x + 3 = 0.This is now a regular quadratic equation that can be solved by factorisation. To factorise, find two numbers whose product is 3 and whose sum is -4. -1 and -3 and to factors of 3 that sum to -4. .Rewrite the equation to be factorised as x2 - 3x - x + 3 = 0.Factorise: x(x - 3) - 1(x - 3) = 0(x - 3)(x - 1) = 0. Set each bracket equal to 0 and solve for the x values. x - 3 = 0, so x = 3 and x - 1 = 0, so x = 1.To find the y values, substitute the x values into y = x + 1.If x = 3, y = 3 + 1 = 4.If x = 1, y = 1 + 1 = 2
