Solve the simultaneous equations - x+y=2 and 4y^2 - x^2 = 11

The objective of simultaeous equations is to be able to work out two unknowns by using two equations in which they are both involved. The first step is to label the equation x+y=2 as equation 1 and 4y- x= 11 as equation 2. Rearrange equation 1 to make one of the unknowns the subject so that we can susbititute this into the second equation leaving only one unknown for us to work out. For example, making x the subject gives us x=2-y and let that be equation 3. Now substitute this into equation 3 giving us the fourth equation 4y2 - (2-y)2 = 11. Expand the brackets giving us 4y2 - (4-4y+y2) = 11 and then further simplify this to give us 3y2 + 4y - 4 = 11. Now subtract 11 from both sides giving us the final quadratic 3y2 + 4y - 15 = 0. Then use the product and sum method of factorising quadratics in order to factorise this equation to (y+3)(3y-5)=0. When the product of two things is zero, it must mean that one of the values equals zero so knowing this means that we know either y+3=0 or 3y-5=0 and so rearranging both gives us that y=-3 or y=5/3. We now use both values of y and substitute them back into equation 3 which is x=2-y to find out both values of x. This gives us x=5 (x=2--3) when y= -3 and x = 1/3 (x=2-5/3) when y= 5/3.

Answered by Keshlee C. Maths tutor

14344 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Water is flowing into a rightcircular cone at the rate r (volume of water per unit time). The cone has radius a, altitude b and the vertex or "tip" is pointing downwards. Find the rate at which the surface is rising when the depth of the water is y.


A curve has the equation, 6x^2 +3xy−y^2 +6=0 and passes through the point A (-5, 10). Find the equation of the normal to the curve at A.


How do I find the co-ordinates of a stationary point of a given line and determine whether it is a minimum or a maximum point?


A curve has the equation y = (x^2 - 5)e^(x^2). Find the x-coordinates of the stationary points of the curve.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences