Term
| How to Determine Which Ordered Pairs Are The Solutions To A Set Of Equations |
|
Definition
| Plug and chug each ordered pair and determine which ordered pairs generate true solutions |
|
|
Term
| How To Determine the Solution to the System of Equations Graphically and find if the system is inconsistent or dependent |
|
Definition
1.)Make sure both equations are in y=mx+b form
2.)Graph Both Lines
3.)If they cross the ordered pair where their cross is the solution for the system of equations and it's consistent
4.)If the lines don't cross they are inconsistent and there is no solution |
|
|
Term
|
Definition
mx=slope aka rise over run
b=y-intercept |
|
|
Term
| How To Solve System of Equations By Substitution Method |
|
Definition
1.)Plug y in for the first equation and solve for x
2.)Plug x into the first equation to solve for y
3.)Write your solution as a solution set |
|
|
Term
How To Solve System of Equations By Substitution Method
When the System is In the Form
ax-by=c
dx-ey=f |
|
Definition
1.)First Solve for a variable in either equation. If possible, solve for a variable with a numerical coefficient of 1 or -1 to avoid working with fractions.
2.) Substitute the expression for the variable you solved for, in the other equation to solve for the other variable.
3.)Apply Distributive Property
4.)Combine Like Terms
5.)If the resulting statement is false it is inconsistent and has no solution. |
|
|
Term
| While Doing A System of Equations If One of the variables is a true statement like a=a, then it has equally many solutions so represent it when you plug it into the next solution as... |
|
Definition
| Itself, then isolate the other variable to one side |
|
|
Term
| How to Solve A System of Equations By The Elimination Method |
|
Definition
1.)Select y as the variable to be eliminated
2.)Multiply both equations by appropriate numbers to get two new equations in which the coefficients of y are opposites.
3.)Add the Two Equations Together
4.)Solve the Resulting equation for x
5.)Substitute the value of x back into one of the original equations to solve for y.
6.)Place your answers in a solution set. |
|
|
Term
| How to Find the X and Y intercepts of Linear Equations |
|
Definition
1.) Set x=0 and solve for the y intercept.
2.) Set y=0 and solve for the x intercept.
3.) The x intercept is formatted as the ordered pair: (x,0)
4.) The y intercept is formatted as the ordered pair: (0,y) |
|
|
Term
*Alternate Method*
How To Determine the Solution to the System of Equations Graphically and find if the system is inconsistent or dependent |
|
Definition
1.)Find the x and y intercept of both linear equations.
2.)Graph Both Lines
3.)If they cross the ordered pair where their cross is the solution for the system of equations
4.)If the lines don't cross they are inconsistent and there is no solution |
|
|
Term
| An independent line is ______ and ______. |
|
Definition
|
|
Term
| Intersecting lines are _______ and independent. |
|
Definition
|
|
Term
| Parallel lines are _______. |
|
Definition
|
|
Term
| An independent line has _____ many solutions. |
|
Definition
|
|
Term
*Alternate Method*
How To Solve System of Equations By Substitution Method
When the System is In the Form
ax-by=c
dx-ey=f |
|
Definition
1.) Substitute one expression for a variable, in the other equation to solve for the other variable.
2.)Apply Distributive Property
3.)Combine Like Terms
4.)Now you should have solved for one of the variables.
5.)Plug the variable you just solved for back into the equation to solve for the other variable.
6.)If the resulting statement is false it is inconsistent and has no solution. |
|
|
Term
| If x=x,is _____, and has _____ many solutions. |
|
Definition
|
|
Term
| Format of a Linear Equation of Two Variables |
|
Definition
|
|
Term
| Linear equations are just... |
|
Definition
|
|
Term
| Whenever you have more unknowns than ____ of linear equations then you have infinitely many solutions |
|
Definition
|
|
Term
How to Find A Value of C that could make a System Consistent: Example
x+2y=7
3x+5y=11
cx+3y=4 |
|
Definition
1.) Find the solution to the subsystem consisting of the first two equations in the system and determine whether or not it is consistent, if so continue, if not there is no solution for c.
2.)Plug in the solution for the subsystem into the third equation of the total system and solve for c. |
|
|
