Solve these simultaneous equations algebraically: y=2x^2 - 7x + 4 & y=4x-1
As we have two equations of x for y we can make these equal to each other. This gives the following:2x2 - 7x + 4 = 4x - 1As with any quadratic we want to make it equal to 0. This gives the following:2x2 - 7x + 4 - 4x + 1 = 0Simplifying this gives:2x2 - 11x + 5 = 0We know want to find two numbers that multiply together to give 5 and when multiplied by 2x and 1x respectively give -11x.There are only two numbers that can give 5 which is 5 and 1. In order to get -11x we need to multiply the 5 by 2x.As the resultant 11x is negative and the 5 positive both 5 and 1 must be negative. This gives the following:(2x-1)(x-5)=0To solve, make each bracket =0.2x-1 = 0 and x-5 = 0x = 1/2 and x = 5Now we have the x values all that needs to be done is to calculate the respective y value. Choose the simplest y equation from the question, which is y = 4x - 1.Therefore when:x = 1/2, y = 4(1/2) - 1 or y = 1x = 5, y = 4(5) - 1 or y = 19
