Graphing 2x2 Systems
Graphing 2x2 Systems 1) 2) 3) 4)
Graph each equation Find the point of intersection if it exists State the solution Check the solution
Solving Systems by Substitution 1) Solve either equation for one of the variables. 2) Substitute this expression into the other equation and solve for the variable - Use the Equation Solver if possible. 3) Substitute the value found in step 2 into either equation for the appropriate variable and solve for the remaining variable. 4) State the solution (ordered pair). 5) Check the solution in both equations.
Example 1)
x 3y 12 2x 4y 9
Example 2)
4x 3y 4 2x y 7
Solving Systems by Elimination 1) Multiply the equations by constants so that something will “cancel.” 2) Add the equations together. 3) Solve the resulting equation. 4) Plug the value back into an original equation to find the other variable. 5) State the solution (ordered pair). 6) Check the solution in both equations
Example 1)
x 3y 12 2x 4y 9
Example 2)
4x 3y 4 2x y 7
Solving Systems Algebraically When solving a system algebraically… If you end up with an equation that is ______________ true, 4≠9
the system has _____________________ (or, it is _________________________ ) or, graphically, the equations’ lines would be ___________________________. If you end up with an equation that is _________________ true,
-24 = -24
the system has _____________________ (or, it is _________________________ ) or, graphically, the equations’ lines would be ___________________________.
Example 1)
5x y 2 10x 2y 9
Example 2)
3x 9y 24 2x 6y 16
Graph each equation Find the point of intersection if it exists State the solution Check the solution
Solving Systems by Substitution 1) Solve either equation for one of the variables. 2) Substitute this expression into the other equation and solve for the variable - Use the Equation Solver if possible. 3) Substitute the value found in step 2 into either equation for the appropriate variable and solve for the remaining variable. 4) State the solution (ordered pair). 5) Check the solution in both equations.
Example 1)
x 3y 12 2x 4y 9
Example 2)
4x 3y 4 2x y 7
Solving Systems by Elimination 1) Multiply the equations by constants so that something will “cancel.” 2) Add the equations together. 3) Solve the resulting equation. 4) Plug the value back into an original equation to find the other variable. 5) State the solution (ordered pair). 6) Check the solution in both equations
Example 1)
x 3y 12 2x 4y 9
Example 2)
4x 3y 4 2x y 7
Solving Systems Algebraically When solving a system algebraically… If you end up with an equation that is ______________ true, 4≠9
the system has _____________________ (or, it is _________________________ ) or, graphically, the equations’ lines would be ___________________________. If you end up with an equation that is _________________ true,
-24 = -24
the system has _____________________ (or, it is _________________________ ) or, graphically, the equations’ lines would be ___________________________.
Example 1)
5x y 2 10x 2y 9
Example 2)
3x 9y 24 2x 6y 16
