How do you solve the simultaneous equations 3x + 4y = 5 and 2x – 3y = 9

We label each equation

3x + 4y = 5 (1)

2x – 3y = 9 (2)

We now want to get rid of one of the variables (x or y). Lets get rid of x:

We need (1) and (2) to have the same number of x's so we multiple (1) by 2 and (2) by 3 so they both have 6 x's

6x + 8y = 10 (1)*2

6x - 9y = 27 (2)*3

Now to get rid of the x's we take one of the equations from the other. It is easier to do (2)*3 -(1)*2

  6x - 9y = 27 (2)*3

- 6x + 8y = 10 (1)*2

                                   

     -17y = 17 

If we devide this equation by -17 we get

y = -1

We can plug this value of y into (1) to get

3x -4 = 5

add 4 to both sides of the equation

3x = 9

Divide by 3

x = 3

Now to check put x and y into (2)

6 - (-3) = 9 

As this is true, we have the solution

x = 3, y = -1

Answered by Sahiti S. Maths tutor

36281 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do you multiply two brackets with two terms in them? For example (2x-3)(x+4)


A cycle race is 3069.25 miles. Juan travels at a speed of 15.12 miles per hour. He cycles for 8 hours a day. Estimate how many days Juan will take to complete the race.


The perimeter of a square is sqrt(120) cm, what is the area?


Solve (3x-2)/4 -(2x+5)/3 =(1-x)/6


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 2013–2024

Terms & Conditions|Privacy Policy