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| A _________ of simultaneous equations is two or more equations to be solved ___ ____ _____ _____. |
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| A system of two linear equations in 2 variables is represented by either: |
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1) Two general equations
2) Two specific equations |
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| The __________ _____ for a system of 2 linear equations in 2 variables is the set of all ordered pairs (x,y) that make both equations _____ ___ ____ _____ _____. |
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| Solution Set, True at the same time |
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| The solution set for a system of 2 linear equations in 2 variables falls into ___ of ____ types. |
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| When the system's graph intersect, the SS will be ... |
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| When the system has no solution, the graphs are ... |
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| The SS is ___________ ______ points when the graphs coincide. |
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| Name the three methods for solving systems of 2 linear equations in 2 variables. |
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A) Graphing Method
B) Linear Combination Method
C) Substitution Method |
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| Name the 4 steps to the graphing method... |
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Definition
1) Rewrite each equation in Slope-Intercept form
2) Graph each equation
3) Determine point of intersection
4)Check the solution |
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| Name the 5 Steps to using the Substitution Method... |
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Definition
1) Solve of of the equations
2) Substitute that expression into the other
3) Solve the resulting equation
4) Back substitute the known value into one of the original equations
5) Check |
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| Name the 5 Steps when using the Linear Combination Method... |
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Definition
1) Arrange like terms in "columns"
2) Rewrite the equations so either the x or y coefficients differ by only a sign.
3) Add the equations.
4) Back substitute
5) Check |
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| If you solve the system by either method and you "loose your variable", the SS will either be: |
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Definition
1) NO SOLUTIONS: if you end up with a false statement - such as 0=5
2) INFINITELY MANY SOLUTIONS ON THE LINE ___________ : if you end up with a true statement - such as 0=0 |
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| The SS for a system of linear inequalities in 2 variables is the set of ___ ______ ______ that make all sentences true ___ ____ _____ _____. |
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Definition
| All ordered pairs, at the same time |
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| Since the solution set is usually an infinite set of ordered pairs, we do what? |
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Definition
| Graph the SS as the intersection of the individual regions, or half-planes. |
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| Name the 3 Steps to Solving a System of Linear Inequalities |
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Definition
1) Graph each inequality and lightly shade the half plane
2) Find the half-plane (region) where the shading overlaps = the solution
3)Pick a point in that region and check to see if it is a solution to all sentences at the same time |
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| A system that has at least one solution is _________ |
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| A consistent system that has exactly one solution is ___________. |
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| A consistent system that has infinitely many solutions is ___________. |
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| If the system has ____ _________, it is inconsistent. |
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| Are you excited for Harry Potter, and find it hard to focus on school work, such as Algebra II? |
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