How to solve a simultaneous equation?

In simultaneous equations, at this level, you are often given two equations both containing an x and a y. For example:Equation1: y + 2x = 3Equation2: 4y + 2x = 8.The first step in approaching this is to try re-arrange one equation with either just y or just x on the left hand side and everything else on the right. Let's rearrange equation 1.We want the equation to read "y =" to do this we need to move "+2x" over to the right hand side. Remember when moving across the equals sign the -/+ sign changes.Our equation now becomes y = 3 - 2xGreat! Now we are almost ready to sub this equation into equation 2! But first note that equation 2 can be simplified further. If we divide through by 2 then we have a simpler equation to solve.. it becomes 2y + x = 4.Now lets put our first equation into this one (substitute in where ever you see y)Joining them together we now get 2(3-2x) + x = 4. Simplyfing this we get, 6 - 4x + x = 4. Then, 2 = 3x.We can use this to find a value for x! lets divide by 3. We now have that x = 2/3.Now that we have solved for one value, we can find the other. To find y, we must put our new value for x into either equation. Let's try it with the first one. y = 3 - 2(2/3). This gives us, y = 3 - (4/3) which is 5/3. (roughly 1.667).If you wanted to be sure of your answers, you can sub them into the other equation and make sure it works!

Answered by Sophie B. Maths tutor

2754 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do I do simultaneous equations?


There are 2 banks, Bank A and Bank B. Bank A provides compound interest of 1.3%. Bank B provides interest of 3.5% for the first year and then 0.7% for each extra year. James wants to invest £250. Which bank provides the most interest after 4 years?


Sketch a graph of the equation of y=3x+2


Solve ((6+x)/2) + ((2-3x)/3) = 31/6


We're here to help

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