Solve the simultaneous equations: 4x+y=25 and x-3y=16

Lets first give the equations names.

4x+y=25 (A)

x-3y=16 (B)

We want to get the equations so that they have either the same number of x's or same number of y's. So let's multiply equation (A) by three so that both equations have 3y in them.

(A) x 3: 12x+3y=75

STOP (Same signs, Take-away. Opposite signs, Plus).

So our 3y's have opposite signs [(A) is +3y and (B) is -3y)] so we need to add these equations together to eliminate all of the y's.

(A) + (B) gives 13x=91

x=91/13, So x=7

We now need to subsitute our value for x into one of the equations to find y.

So subbing x=7 into equation (B) gives:

7-3y=16

7-16=3y

-9=3y

y=-3

So our solution is x=7, y-3.

We can now check our solution by subbing these values into the other equation. So subbing x=7 and y=-3 into (A) gives 4(7)+(-3)=25. This means our solution for the simultaneous equation is correct because these values also work for equation (A).

Answered by Michael D. Maths tutor

8520 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

where do the graphs y=3x^2-2x-5 and y=4x-2 intersect


Prove that (4x–5)^2 – 5x(3x – 8) is positive for all values of x.


How can you solve an equation with unknowns in the denominators?


Describe and explain three adaptations of succulent plants that allow them to live in hot and dry conditions.


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