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# How do you solve simultaneous equations where both equations are linear?

2 years ago

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Celestino Spinka

1 Answer

Ante R
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Professional Engineer with years of experience, especially in tutoring

A method that always works is to express one variable as a function of another, and then substitute that expression into the other equation.

**Example:**

[1] x+y = 5

[2] 2x+3y = 8

[1] x = 5-y

[1] -> [2] 2(5-y)+3y = 8

10-2y+3y = 8

y = -2

x = 5-(-2) = 7

Solution: (7, -2)

Note: There are other ways of solving these kinds of equations, depending on the coefficients, but this method always works.

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