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 having had previous experience assisting younger students in Maths classes alongside being a swimming teacher for nearly five years, I would be able to offer a friendly and beneficial service.

__The Sessions__

During the sessions the main focus will be to **improve the basic understanding of the topic**. This will be done flexibly depending on the student and the ways they learn best. Once the understanding is in place the student will be **guided through a large variety of exam questions and how to obtain the maximum number of marks**.

__Oxbridge Applications__

Having been through the application process myself I can offer **extensive assistance in writing personal statements** and **preparing for the PAT entrance exam**.

__Next Step__

**If you have any questions send me a Webmail or book a ‘Meet the Tutor’ session. Let me know what topics and questions you require assistance with and we can move on from there!**

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 having had previous experience assisting younger students in Maths classes alongside being a swimming teacher for nearly five years, I would be able to offer a friendly and beneficial service.

__The Sessions__

During the sessions the main focus will be to **improve the basic understanding of the topic**. This will be done flexibly depending on the student and the ways they learn best. Once the understanding is in place the student will be **guided through a large variety of exam questions and how to obtain the maximum number of marks**.

__Oxbridge Applications__

Having been through the application process myself I can offer **extensive assistance in writing personal statements** and **preparing for the PAT entrance exam**.

__Next Step__

**If you have any questions send me a Webmail or book a ‘Meet the Tutor’ session. Let me know what topics and questions you require assistance with and we can move on from there!**

We only take tutor applications from candidates who are studying at the UK’s leading universities. Candidates who fulfil our grade criteria then pass to the interview stage, where a member of the MyTutor team will personally assess them for subject knowledge, communication skills and general tutoring approach. About 1 in 7 becomes a tutor on our site.

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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.

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.