Solving simultaneous allows us to determine the value of two variables from two equations. 2x+y = 133x+2y = 21
To find the value of the variables, our first step is to choose a variable and have equal numbers of this variable in both of the equations. There are a number of ways we can alter the equations, but to ensure the equation remains equal we must alter both sides of the equations equally. e.g. -5 from both sides, +2x to both sides, both sides multiplied by two.
It is easiest to equate the y variable, as we can have 2y in both equations while only altering one equation (less chance of making a mistake!).
Multiplying the first equation by two:2(2x+y) = 2*134x+2y = 26
We then subtract the equation with the smaller number from the other. 4x+2y = 263x+2y = 21This works the same as a normal subtraction2y-2y = 0 and 26-21 = 5This leaves us with x=5
We can also write the equations as being equal to 0, for example4x+2y = 264x+2y - 26 = 03x+2y = 213x+2y - 21 = 0
Both equations now equal zero, so they are equal to each other4x+2y - 26 = 3x+2y - 21By subtracting 2y from both sides and adding 26 to both sides, we reach the same resultx = 5
Substituting x= 5 back into one of the original equations2x+y = 1310+y = 13y = 3
We can check this answer using the other equation (just to be sure)3x+2y = 2115+6 = 2121 = 21
We have found each of the variables and checked them. The correct answer is x = 5, y = 3

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