Term
How do you determine what ordered pairs are solutions of a system of equations?
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Definition
1.)Plug in each ordered pair, into each equation in the system.
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2.)If an ordered pair generates a true solution when plugged into each system of equations, then it acts as a solution to a system of equations.
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Term
Which Ordered Pairs (1,-A),(A,B), and (0,0) are Solutions of the following system of equations?
-Bx+Ay=0
Ax+y=0
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Definition
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Term
How do you graph a linear equation, that is not already in y=mx+b, form?
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Definition
1.)Isolate "y" on one side of an equal sign.
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2.)Graph a point at (0,b)
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3.)Move "m" units up from (0,b) and one unit to the right.
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Term
When a system of equations has one solution, where do you find that solution on the graph?
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Definition
The coordinates of the point of intersection give the solution.
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Term
When does a system of equations have no solution?
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Definition
When the lines are parallel, aka inconsistent.
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Term
When a system of equations have an infinite number of solutions?
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Definition
If two lines are identical
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Term
How do you graph this equation?
y=mx+b
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Definition
1.)Graph a point at (0,b)
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2.)Move "m" units up from (0,b) and one unit to the right.
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Term
How do you solve the following system of equations by the substitution method?
Ax-By=C
Dx+E=y
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Definition
1.)Insert the equation that equals "y" in for "y" into the other equation, and solve for "x".
Ax-B(Dx+E)=C
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2.)Plug the value of "x", that was solved in the following equation, into the equation that equaled "y". Solve for "y".
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3.)Write the solution to the system of equations as an ordered pair.
("x" value, "y" value)
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Term
If a system of equations is inconsistent, then the system will have how many solutions?
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Definition
No solution, it will generate a false statement.
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Term
If this system of equations, when using the elimination technique generates 0=0, what is the solution?
x-Ay=B
-Cx+Dy=-E
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Definition
Infinitely many solutions
[x,1/A(x-B)], where "x" is any real number.
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Term
How do you solve a system of equations by elimination?
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Definition
Edit the equations to where when they are added together, a variable is eliminated, then solve for the remaining variable, and re-insert the solved variable into one of the variables and solve for the other variable.
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Term
If a system of equations is inconsistent, if the solution statement is what?
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Definition
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Term
If this system of equations, when using the elimination technique generates 0=0, what is the solution?
Ax+By=C
Dx+Ey=F
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Definition
x,((C-Ax)/B) where "x" is any real number
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