885 views

### Find x and y of these two equations: 2x - 3y = 13 and 3x + y = 3

In order to find the unknown variables x and y we need to simplify these equations in the way that will make it possible for us to get rid of either x or y variable, and make it easier to solve the remaining variable.

This method is known as Elimination, which is one of the methods how to solve a system of linear equations.

We need to rewrite the equations so that when the equations are added, one of the variables is eliminated. In simple terms, we need to get same number of x's or the same number of y's, but with an opposite sign, in both equations.

(1) 2x - 3y =13

(2) 3x + y = 3

You can multiply equation (2) by 3, then add equations (1) and (2) to form equation (3) with just one variable.

(2) 3*(3x+y) = 3*(3)

(2) 9x + 3y = 9

(1) 2x - 3y = 13

(3) 9x + 3y + 2x - 3y = 9 + 13

(3) 11x = 22

(3) x = 2

Then substitute our value for x back to one of the original equations and find what the value of y is.

2x - 3y = 13

2*(2) - 3y = 13

4 - 3y =13

- 3y = 9

y = - 3

Afterwards we can check our results by substituting our variables back into the original equations.

2*(2) - 3*(- 3) = 13

3*(2) + (- 3) = 3

Problem solved :)

1 year ago

Answered by Zuzana, a GCSE Maths tutor with MyTutor

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

#### 618 SUBJECT SPECIALISTS

£36 /hr

Degree: Architecture and Environmental Engineering (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Design & Technology
-Personal Statements-

“Hi there, I have a passion for helping students achieve, and believe that with my 200+ hours of experience, we will be able to surpass the grades you want!”

£30 /hr

Degree: Dentistry (Masters) - Leeds University

Subjects offered:Maths, Science+ 12 more

Maths
Science
Mandarin
Human Biology
English Literature
English Language
Chemistry
.UKCAT.
-Personal Statements-
-Oxbridge Preparation-
-Medical School Preparation-

“Hi I'm Vicky, I'm a 2nd year dental student at the University of Leeds. I am friendly and patient and have a love for science, maths and teaching.”

£30 /hr

Degree: Law (Bachelors) - Durham University

Subjects offered:Maths, Business Studies+ 2 more

Maths
.LNAT.
-Personal Statements-

“Durham law graduate with four years tutoring experience in a wide range of subjects. ”

Currently unavailable: for regular students

Degree: Biomedical Sciences with Management (Medical Biology) (Bachelors) - Edinburgh University

Subjects offered:Maths, Science+ 3 more

Maths
Science
Human Biology
-Personal Statements-

“About me: I have always found science very interesting and later realizing that understanding of it may have a significant impact on my life made me want to dig into scientific field more. Once you understand the principles, it can he...”

MyTutor guarantee

### You may also like...

#### Posts by Zuzana

Describe the passive movement through diffusion and explain Fick's Law

Find x and y of these two equations: 2x - 3y = 13 and 3x + y = 3

What are the major parts of a neuron? What are the three types of nerve cells?

#### Other GCSE Maths questions

What are the differences between arithmetic and geometric sequences?

work out the value of 4a + 2b when a = 4 and b = 3

How do I factorise x^2 ​- 4?