Whenever we want to solve a system of equations we need to choose a method that we want to use. Sometimes one method seems to be easier to use when solving than others. Let's take a look at the example systems of linear equations.
System
Method
y=2x-3 y=x+2
?
x=6-y 2x+4y=10
?
2x-4y=9 - 3x+4y=7
?
In the first system both equations are in slope-intercept form. Therefore it might be easier to solve this system by graphing.
System
Method
y=2x-3 y=x+2
Graphing
x=6-y 2x+4y=10
?
2x-4y=9 -3x+4y=7
?
In the second system, Equation 1 is solved for x. This means that we can use substitution and substitute the value of x into the other equation.
System
Method
y=2x-3 y=x+2
Graphing
x=6-y 2x+4y=10
Substitution
2x-4y=9 -3x+4y=7
?
Finally, in the third system one pair of variable terms have opposite coefficients. Therefore, the y-terms will eliminate each other when we add the equations, and elimination seems to be the easiest method.
System
Method
y=2x-3 y=x+2
Graphing
x=6-y 2x+4y=10
Substitution
2x-4y=9 -3x+4y=7
Elimination
Summing up, it might be easier to solve a system of equations by elimination instead of graphing if it has at least one pair of variable terms with opposite coefficients.
