MYTUTOR SUBJECT ANSWERS

215 views

Solve the simultaneous equations 4x + 7y = 1 and 3x +10y = 15.

There are two main ways of solving this equation, substitution and elimination, here we go through the susbtitution method. This involves rearranging one of the equations to get one of the variables in terms of the other, for example x in terms of y. We then substitute this new expression for x into the other equation and rearrange to solve for y. We then use the value of y in either equation to solve for x.

Rearrange the first equation for x:

4x = 1 - 7y

x = (1-7y)/4

Subsitute x into the second equation:

3*((1-7y)/4) + 10y = 15

Expand the brackets:

(3/4)*(1-7y) + 10y = 15

3/4 -21y/4 + 10y = 15

Collect like terms (write 10y as 40y/4 and 15 as 60/4):

40y/4 - 21y/4 = 60/4 - 3/4

19y/4 = 57/4

Multiply by 4:

19y = 57

Rearrange for y:

y = 57/19 = 3

Subsitute y = 3 into either equation, we use the second:

3x +10*3 = 15

3x + 30 = 15

3x = 15 - 30

3x = -15

x = -15/3 = -5

Finally write the answers out:

x = -5 and y = 3.

Luke C. GCSE Physics tutor, GCSE Maths tutor

6 months ago

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

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

328 SUBJECT SPECIALISTS

£18 /hr

Jasmine S.

Degree: Mathematics (Bachelors) - Exeter University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hi, I'm Jasmine and I'm a second year Mathematician at Exeter University, I'm looking to help students prepare for their Maths and Physics exams.”

£18 /hr

David S.

Degree: Engineering (Masters) - Warwick University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About MeI am a first year engineering student at the University of Warwick, I enjoy maths and physics. I am patient, reliable and flexible to suit you but the focus of my tutoring is instilling confidence into a student as they work....”

£18 /hr

Charles B.

Degree: Classics (Bachelors) - Durham University

Subjects offered: Maths, Latin+ 1 more

Maths
Latin
Classical Civilisation

“About me I'm a passionate classicist particularly focused on ancient military warfare  currently studying classics at Durham University. I've been studying Latin and  Ancient History since I was 9 years old, picking up Ancient Greek at ...”

About the author

£18 /hr

Luke C.

Degree: Physics with Astronomy (Masters) - Nottingham University

Subjects offered: Maths, Physics

Maths
Physics

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

MyTutor guarantee

You may also like...

Posts by Luke

Solve the simultaneous equations 4x + 7y = 1 and 3x +10y = 15.

Why does lowering the control rods in a nuclear reactor reduce the amount of energy released each second from the nuclear fuel?

Other GCSE Maths questions

There are 5 white socks and 3 black socks in a draw. Steven takes out 2 at random. Work out the probability that Steven takes out 2 socks of the same colour.

Solve x^2 - 7x + 10 = 0

Factorise x² + 2x - 8

Solve the simultaneous equations 2x + y = 7 and 3x - y = 8.

View GCSE Maths tutors

Cookies:

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

mtw:mercury1:status:ok