Term
| How to Determine Whether An Ordered Triple is a Solution of a System of Equations When An Ordered Triple is Provided Alongside A System of Equations |
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Definition
1.) Plug and Chug The Ordered Triple Into Each Equation in the System
2.) If any of the equations produce false statements, then the Ordered Triple is not a Solution of the System of Equations.
3.)If all three equations produce true statements, then the Ordered Triple is a solution to the system of equations. |
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Term
| Format Of An Ordered Triple |
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Definition
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Term
| How to Solve A Triangular Linear System in Which You Are Provided With A System of Two Equations and One Variable Solved |
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Definition
1.)Note the Solved Variable
2.)Substitute the Solved Variable Into The Second Equation In The System, Simplify, and Solve for the Remaining Variable in that Equation.
3.)Plug in the already solved variable and the variable you just solved for into the first equation, simplify, and solve for the remaining variable.
4.)Verify that the solutions for (x,y,and z) are correct by plugging them back into the first equation and second equation, if the statements are true then they are the solutions to the system of equations, if the resulting statements are false then they are not the solutions of the system of equations. |
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Term
| How to Find The Solution Set of Each Linear System When Provided With Three Linear Equations |
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Definition
1.)Convert the System of Equations Into Triangular Form
2.) Solve The Triangular Linear System in Which You Are Provided With A System of Two Equations and One Variable Solved |
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Term
| Format of Triangular Form |
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Definition
x+ay+bz=p
y+cz=q
z=zsubscrpt0 |
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Term
| How to Convert A System of Equations Into Triangular Form |
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Definition
1.)Note the leading coefficient of x in the (first) equation
2.) Eliminate x in the second equation by multiplying both sides of the first equation by the negative form of the coefficient of the first equation and adding it to the second equation which should form something like y+cz=q which will now be known as equation 4.
3.)Eliminate x in the third equation by multiplying both sides of the first equation by the negative form of the coefficient of the first equation and adding it to the third equation which should form something like y+cz+q which will now be known as equation five.
4.)You now have a new System of Equations which is composed of the first equation, equation four, and equation five.
5.)Now eliminate the y term from equation five by multiplying both sides of equation four by the negative form of equation five's coefficient and add it to equation five which once simplified will result in an equation in the form of z=zsubsrcpt0, which will now be known as Equation Six.
6.)Now you have a triangular form of the given system of equations composed of equation one, equation four, and equation six. |
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Term
How to Find The Quadratic Function
y=ax^2+bx+c
Whose Graph Passes Through a Set of Given Points Represented by Three Ordered Pairs |
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Definition
1.)Plug the first ordered pair into y=ax^2+bx+c
And Simplify to Form A New Equation
2.)Plug the second ordered pair into
y=ax^2+bx+c
And Simplify to Form Another New Equation
3.)Plug the third ordered pair into
y=ax^2+bx+c
And Simplify to Form Another New Equation
4.)The resulting three equations formed is a linear system in three variables.
5.)Find the solutions to the system of equations
6.)Plug the solutions of the system back in to
y=ax^2+bx+c
form and simplify to find the quadratic function |
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Term
| If multiple linear equations in a system of equations are equal then there are... |
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Definition
| infinitely many solutions |
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