Solve the simultaneous equations y= 3x +4 and y= 2x + 5

'Solve' means to find the values of the unknown variables in the equations, commonly letters, which in this question are x and y.

Step 1: Put equations equal to eachother

Both equations given are equal to y (written in the form y=), therefore we can put the parts containing x of the equations equal to each other, giving 3x+4 = 2x+5

Step 2: Collect 'like' terms

All this means is to get all of the terms containing x (or letter given in the question) on one side, and all the numbers on the other side.

So in this example, to get all the x's on one side we can subtract 2x from both sides giving x+4 = 5.

And to get all the numbers on the other side, we can subtract 4 to both sides giving x=1

Step 3: Solve

In this example, we have already managed to find out the value of x from step 2 (x=1)

To find out y, we can substitute in our calculated x value into any of the equations given (it is usually quicker and easier to use the equation with smaller numbers!)

So, using the second equation, and substituting in x=1, we can calculate the value of y. 

y = 2(1)+ 5 = 2+ 5 = 7  giving y=7

Step 4: Check

In an exam, if you have time, it is always worth checking you have calculated the correct answers!

This is easy, just substitute your calculated values of x and y into both equations, and if correct, then each side will be equal to each other. 

For example:

7 = 3(1) +4  = 3 + 4 = 7 

7 = 2(1) + 5 = 2 + 5 = 7

Both sides are equal to each other therefore this is correct!

Vicky C. GCSE Biology tutor, GCSE Chemistry tutor, GCSE Maths tutor, ...

1 year ago

Answered by Vicky, who has applied to tutor GCSE Maths with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£22 /hr

Nicolo G.

Degree: BSc Government and Economics (Bachelors) - LSE University

Subjects offered: Maths, History+ 2 more


“I am currently a student of economics and government at the London School of Economics. I developed a passion for economics during my IB diploma studies and I hope I will be able to instill that passion in you as well. I am very patien...”

£18 /hr

Luke C.

Degree: Biological Sciences with a year in professional placement (Bachelors) - Exeter University

Subjects offered: Maths, Physics+ 2 more


“My greatest passion is for biology, but I have always enjoyed studying chemistry and mathematics too. Studying these subjects has supported me during my time so far at Exeter University, even though I am still in my first year of stud...”

£20 /hr

Rachael O.

Degree: Medicine (Other) - Bristol University

Subjects offered: Maths, Science+ 6 more

Human Biology
-Personal Statements-
-Medical School Preparation-

“Hi, my name's Rachael and I'm 21. I am a 3rd year medical student studying at Bristol University.  Availability: Mon-Fri 7pm-9pm (excluding Wednesdays). Weekends negotiable.  My aim is to help students enjoy learning and feel confid...”

About the author

£18 /hr

Vicky C.

Degree: Biology (Bachelors) - Durham University

Subjects offered: Maths, Further Mathematics + 2 more

Further Mathematics

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

Point A (-3,5) and point B (1,-15) are to be connected to form a straight line, fing the equation of the line in the form y=mx+c?

How Would I Factorise A Quadratic Equation?

Jill takes out a loan of £6000 to get a car. The loan has a compound interest of 3% and she takes it out for 4 years. a) How much interest has Jill accrued after 2 years? b) What is the total amount to be paid after 4 years?

Solve the simultaneous equations '2X+Y=7' and '3X-Y=8'

View GCSE Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss