Solve the simultaneous equations y = x^2 +3x and y = x+8

Because both of the equations are equal to y, the first thing we do is make them equal to each other:x^2 + 3x= x + 8We then want to rearrange the equation so that everything is on the same side of the equals sign, so that the equation is equal to 0:x^2 + 3x - x - 8 = 0We can then simplify this down to be:x^2 + 2x - 8 = 0The simplest method to find x from the above equation is to factorise. This is where we create two sets of brackets from the equation. To put the equation into brackets, we need to find two numbers that multiply together to make -8 and add together to make 2. These numbers are +4 and -2, which are put into the brackets as follows:(x+4)(x-2) = 0If the product of two brackets is 0, then one or both brackets must also be equal to 0. To solve, put each bracket equal to 0:x+4 = 0x = -4x-2 = 0x = 2To find the value for y, substitute these values of x back into the original equation.y = x + 8 when x = -4y = -4 + 8 y = 4y = x + 8 when x = 2y = 2 + 8y = 10The answers are now in pairs: when x = -4, y = 4 and when x = 2, y = 10

JW
Answered by Jessica W. Maths tutor

3672 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

A stationary ball starts rolling down a hill, and after 5s it reaches a speed of 12m/s. From here the ground levels off, and the ball continues at this speed for 3 more seconds. Plot this on a velocity-time diagram.


Insert one pair of brackets so that this calculation is correct; 3 x 6 + 5 - 1 = 32


A car costs £1200 in a sale. It was reduced by 20%. What was the original price?


How do I find the length of a side of a triangle using the cosine rule?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences