11.5 Summary of key concepts

Summary of key concepts

System of equations ( [link] )

Solution to a system ( [link] )

Independent systems ( [link] )

Inconsistent systems ( [link] )

Dependent systems ( [link] )

Solving a system by graphing ( [link] )

1. Graph each equation of the same set of axes.
2. If the lines intersect, the solution is the point of intersection.

Solving a system by substitution ( [link] )

1. Solve one of the equations for one of the variables.
2. Substitute the expression for the variable chosen in step 1 into the other equation.
3. Solve the resulting equation in one variable.
4. Substitute the value obtained in step 3 into the equation obtained in step 1 and solve to obtain the value of the other variable.
5. Check the solution in both equations.
6. Write the solution as an ordered pair.

Solving a system by addition ( [link] )

1. Write, if necessary, both equations in general form
   
   $ax+by=c$
2. If necessary, multiply one or both equations by factors that will produce opposite coefficients for one of the variables.
3. Add the equations to eliminate one equation and one variable.
4. Solve the equation obtained in step 3.
5. Substitute the value obtained in step 4 into either of the original equations and solve to obtain the value of the other variable.
6. Check the solution in both equations.
7. Write the solution as an ordered pair.

Substitution and addition and parallel lines ( [link] , [link] )

Substitution and addition and coincident lines ( [link] , [link] )

Applications ( [link] )