MYTUTOR SUBJECT ANSWERS

356 views

Solve the simultaneous equations 5x+2y=11 and x-y=-2.

Simultaneous Equations are equations involving 2 or more unknowns that are to have the same value in each equation. The aim is to eliminate all except one unknown which will then allow us to find the value of that unknown. From this any other unknowns can be found. There are 2 main methods we can use to solve these problems:

1.Solving by Elimination

This method works due to 2 properties of equations:

1.Multiplying or dividing the expression on each side by the same number does not alter the equation.

2.Addition of 2 equations produces another valid equation.

We must manipulate the 2 equations so that when added or subtracted an unknown is removed. First we must label our equations:

(1)5x+2y=11

(2)x-y=-2

Now we must manipulate one or both of the equations so we can remove an unknown by elimination.

For example here the easiest method would be to multiply equation (2) by 2 to obtain equation (3)2x-2y=-4. Then by adding equation (1) to equation (3) we would eliminate y from our equations.

This would give us 7x=7. Therefore we can see that x=1.

Now we substitute this value of x back into either of our original equations (1) or (2). If we substitute back into (2) we obtain the equation 1-y=-2. From this we can see that y=3.

Therefore we have solved the simultaneous equations and obtained the answer of x=1 and y=3.

2.Solving by Substitution

This involves making one of the variables the subject of the equation then substituting this equation into the other simultaneous equation hence removing one of the unknowns.

For this equation if we make x the subject in equation (2) we obtain x=y-2. Then by substituting this x expression into equation (1) we obtain 5(y-2)+2y=11.

By expanding the bracket and collecting like terms we obtain the equation 7y=21. We can see from this that y=3.

Then similarly to before we substitute this y value back into either equation (1) or (2).

If we substitute back into equation (2) we obtain the equation x-3=-2.

We can see from this that x=1.

Therefore we have obtained the answer of x=1, y=3 which is the same as for solving by elimination.

For simple simultaneous equation problems such as this one, elimination is often the more efficient method. However as problems become more complex substitution is often required as integers may not always be used.

Peter H. GCSE Maths tutor, A Level Maths tutor, GCSE Physics tutor, A...

7 months ago

Answered by Peter, a GCSE Maths tutor with MyTutor


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

330 SUBJECT SPECIALISTS

£20 /hr

Cesar Manuel F.

Degree: BSc Computer Science (Bachelors) - University College London University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
History
Computing

“Hello! My name is Cesar, I am originally from Perú but I currently study BSc Computer Science at University College London. I graduated Markham College with Distinction after completing my International Baccalaureate (IB) course, in w...”

£18 /hr

Jake B.

Degree: Mathematics (Masters) - Durham University

Subjects offered: Maths, Chemistry

Maths
Chemistry

“About Me: Hi, my name is Jake, and I am a second year Mathematics Student at Durham University. I have tutored maths for 3 years now, at both GCSE and A level, and I absolutely love it! I My Sessions: During the sessions I will cove...”

MyTutor guarantee

£18 /hr

Adam T.

Degree: Physics (Bachelors) - Edinburgh University

Subjects offered: Maths, Physics

Maths
Physics

“About Me I am currently studying Mathematical Physics at the University of Edinburgh.  I find physics and maths interesting and exciting and I hope I can show you how intriguing and entertaining your course can be as well.   When stu...”

MyTutor guarantee

About the author

Peter H.

Currently unavailable: for regular students

Degree: Engineering Science (Masters) - Oxford, Balliol College University

Subjects offered: Maths, Physics+ 5 more

Maths
Physics
Further Mathematics
Electronics
Biology
.PAT.
-Personal Statements-

“I am a second year Engineering Science student at Balliol College, Oxford University. One of the most appealing features of studying engineering is being able to apply Mathematics and Physics theory to real world problems. I feel that...”

You may also like...

Other GCSE Maths questions

Solve (x + 2)(x+3) = (2x+4)

Solve these simultaneous equations (2x+y=7 and 3x-y=8) and find the values of Equation: x and Equation: y .

What is Pythagorus' Theorem?

Bag A contains £7.20 in 20p coins. Bag B contains only 5p coins. The number of coins in bag B is three-quarters of the number of coins in bag A. How much money is in bag B?

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