BOUNOMICS - SIMULTANEOUS EQUATIONS

--AIM--

"To solve a system of two linear equations in two variables using the elimination method (also called the addition method), we combine the equations in such a way that one variable cancels out..”

--SUGGESTED STEPS--

"Let's use these two equations!"

(1) 3x + 2y = 8

(2) x − y = 1

It is vital for you to understand that these two equations can be combined like this:

If 3x + 2y = 8 AND x − y = 1

Then, (3x + 2y) + (x − y) = 8 + 1,

Step 1: Align the coefficients of variable 'x' or 'y':

In this case let's 'ELIMINATE' the value of the 'y' variable in both (1) and (2), to do this we need to have the same valued y-variable in both equations with one being POSITIVE and the other being NEGATIVE.

So because equation (1) has a positive y-variable of '+2y' then, we need to get a negative y-variable of '-2y' in equation (2). To do this we multiply all the parts of equation (2) by 2...

(2) x (x2) − y (x2) = 1 (x2), becomes

2x - 2y = 2,

We can see that the y-variable is now = 2y, which is the same as the y-variable in equation (1).

Step 2: 'Combine' the equations (1) + (2) to 'eliminate' that variable.

(3x + 2y) + (2x − 2y) = 8 + 2, becomes

5x = 10

Step 3: Solve for the chosen variable.

5x = 10

divide both sides by

x = 2

Step 4: Subsititute variable value into (1) or (2).

Let's substitute the value of Step 3, which was X = 2 into equation (2) to work out 'y':

(2) x − y = 1, becomes

2 - y = 1, therefore

y = 1

TASK:

You will be assigned a question to work through step-by-step and post your process on the Padlet below. You may use the example given as a guide on how to structure your answer.

--WORKSHEETS--

"Now CHOOSE 5 simultaneous equations from the worksheet below and complete in your books using the 'elimination method', and of course show your workings."

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