Asked • 01/25/25

What are the three methods used to solve systems of equations?

Evan C.

tutor
Hi! There are 3 methods used to solve systems of equations. 1) Graphing- Graphing involves graphing the functions involved in the system and finding the point that they intersect. If there is one intersection, that is the solution. If the lines are parallel, no solution, and if they are the same line, they will have infinite solutions. 2) Substitution- In this case we will have one equation as a variable alone on one side of an equal sign. For example: y=5x+3 2y+3x=8 Since y=5x+3, we can use substitution to replace y in the second equation with "5x+3" as follows: 2(5x+3) +3x=8. now we only have x in this equation, so we can solve for this variable and then use it to solve for y. 3) Elimination- This strategy involves subtracting one equation from the other, or adding them together in order to eliminate one of the variables and solve for the second variable. For example: 2y+3x=8 2y+7x=16 In this case we will subtract the equations from each other. 2y-2y cancels out. 3x-7x gives us -4x. 8-16 gives us -8. This gives us -4x=-8, which we can then solve to find that x=2. Once we find that x = 2, we can plug it back in to either of the original equations to solve for y.
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01/25/25

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Frank T. answered • 01/28/25

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