If 2x + y = 13 and 3x + 2y = 21, work out the values of x and y.

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Equation 1: 2x + y = 13

Equation 2: 3x + 2y = 21

Multiply 'equation 1' by 2 gives: 4x + 2y = 26

4x + 2y = 26 can be equation 3.

Subtract equation 3 from equation 2, gives x = 5. 

By doing this, you eliminate the y and therefore are left with the value of x.

So if x = 5, then put x=5 into 'equation 1'.

2(5) + y = 13.

10 + y = 13

Subract 10 from both sides and you're left with

y=3.

Now check your answers are right by putting x=5 and y=3 into 'equation 2'. 

3(5) + 2(3) = 21.

15 + 6 = 21.  Correct. Therefore X=5 and Y=3.

Matthew S. GCSE Biology tutor, GCSE Chemistry tutor

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