you are learning about systems of equations and three methods for solving them:

Question

you are learning about systems of equations and three methods for solving them: graphing, substitution, and addition. Compare and contrast the three methods by discussing the following: Is one method easier than the others for all systems, or does it depend on the system? If it depends on the system, how could you tell before you begin solving the system which solution method would be the most efficient? How is it possible to tell by inspection (look at it) whether a system of linear equations has one, zero, or an infinite number of solutions?

Explanation / Answer

taking an example of equations

x = y + 2

2x + 3y = 5

in substitution method we substitute value of x from equation 1 into equation 2

and in this way we get one equation in terms of just one variable and we can solve it easily

in addition method we eliminate one variable by making coefficients of the variable we want to eliminate equal and opposite

and in graphing method we graph each equation and see where the two lines intersect

that will be solution

when solving equation by substitution and addition

if left hand side = right hand side

this means equation has infinite solutions

if we get all variables eliminated and left side is not equao to right side it means it has no solution

when solving by graphical method

if we get graph of two lines same

then it means it has infinite solutions

if we get two parallel lines

it has no solution

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