If 2x + y = 13 and 3x - y = 12, what are the values for x and y?

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To solve these simulataneous equations we need to use substitution:

If 2x + y = 13 then y = 13 - 2x

Therefore 3x - y = 12 can be rewritten as 3x - (13 - 2x) = 12

We can expand these brackets and solve for x:

3x - 13 + 2x = 12

-> 5x = 25

--> x = 5

Now we have the value of x, we can subsitute this into either of the initial equations to find the value of y:

2(5) + y = 13

--> 10 + y = 13

--> y = 3

OR:

3(5) - y = 12

--> 15 - y = 12

--> y = 3

You can then check your values are correct by subsituting them into either of the equations:

2(5) + (3) = 13

10 + 3 = 13 --> it works!

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