Question:
Solve the following set of simultaneous equations: x + 3y = 10 2x + y = 5
Methods:
Firstly, multiply eq.1 by 2, to obtain: (eq.3) 2x + 6y = 20
Next, subtract eq.2 from eq.3 to obtain: (eq.4) 5y = 15
Next, divide eq.4 by 5 to obtain: y = 3
Now substitute y = 3 into any of the previous equations, for example, using eq.2 we get: (eq.5) 2x + 3 = 5
Now solve eq.5 by subtracting 3 from both sides:
2x = 2
Then divide by 2:
x = 1
Now we have our unique solution to the pair of simultaneous equations: x = 1, y = 3.
We can check the solution works by substituting back into one of the first two equations, e.g., in eq.1: x + 3y = 1 + (3×3) = 1 + 9 = 10
Answer:
x = 1 y = 3
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