can you explain 4 method to solve a system of equations?

Answer 1

Addition Method

ax + by = c
dx + ey = f

(ax + by) + (dx + ey) = c + f

Solve for one variable, then substitute that into one of the equations above.

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Subtraction Method

ax + by = c
dx + ey = f

(ax + by) - (dx + ey) = c - f

Now solve and substitute like you did in the Addtion Method

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Elimination Method

ax + by = c
dx + ey = f

Multiply either the top, bottom, or both in order to get either the coefficents of x or y so that they are opposite to each other.

ax + by = c
-ax - ey = -f

by - ey = c - f
y(b - e) = c - f
y = (c - f)/(b - e)

Now substitute (c - f)/(b - e) in for y into any of the equations and solve for x

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ax + by = c
dx + ey = f

ax + by = c
by = -ax + c
y = (-ax + c)/b

Now substitute that in for y, then solve for x, now substitute the x value into y = (-ax + c)/b in order to get y's value.

Answer 2

Actually, there are seven methods to solve a system of linear equations. However, explaining all seven methods in this forum would be extremely difficult.

The methods are: Graphing, Substitution, Elimination (sometimes called Addition), Gaussian Elimination, Gauss-Jordan elimination, Matrix Inverse, and Cramer's Rule.

Answer 3

Are they linear system?