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Algebraic Method

Algebraic Method

What Is the Algebraic Method?

The algebraic method alludes to different methods of tackling a pair of linear equations, including graphing, substitution and elimination.

What Does the Algebraic Method Tell You?

The charting method includes diagramming the two equations. The crossing point of the two lines will be a x,y coordinate, which is the solution.

With the substitution method, revamp the equations to express the value of variables, x or y, in terms of another variable. Then, at that point, substitute that expression for the value of that variable in the other equation.

For instance, to address:
8x+6y=16โˆ’8xโˆ’4y=โˆ’8\begin &8x+6y=16\ &{-8}x-4y=-8\ \end
To start with, utilize the second equation to express x in terms of y:
Then substitute 1 - 0.5y for x in the primary equation:
8(1โˆ’0.5y)+6y=168โˆ’4y+6y=168+2y=162y=8y=4\begin &8\left(1-0.5y\right)+6y=16\ &8-4y+6y=16\ &8+2y=16\ &2y=8\ &y=4\ \end
Then supplant y in the second equation with 4 to tackle for x:
8x+6(4)=168x+24=168x=โˆ’8x=โˆ’1\begin &8x+6\left(4\right)=16\ &8x+24=16\ &8x=-8\ &x=-1\ \end
The subsequent method is the elimination method. It is utilized when one of the variables can be killed by either adding or taking away the two equations. On account of these two [equations](/bookkeeping equation), we can add them together to wipe out x:
8x+6y=16โˆ’8xโˆ’4y=โˆ’80+2y=8y=4\begin &8x+6y=16\ &{-8}x-4y=-8\ &0+2y=8\ &y=4\ \end
Presently, to settle for x, substitute the value for y in one or the other equation:
8x+6y=168x+6(4)=168x+24=168x+24โˆ’24=16โˆ’248x=โˆ’8x=โˆ’1\begin &8x+6y=16\ &8x+6\left(4\right)=16\ &8x+24=16\ &8x+24-24=16-24\ &8x=-8\ &x=-1\ \end


  • The most-generally utilized algebraic methods incorporate the substitution method, the elimination method, and the charting method.
  • The algebraic method is an assortment of several methods used to settle a pair of linear equations with two variables.