Solve Systems of Linear Equations
8th Grade
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Pennsylvania Core Standards:
CC.2.2.8.B.3
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Analyze and solve linear equations and pairs of simultaneous linear equations. |
Pennsylvania Core Standards:
M08.B-E.3.1.3
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Interpret solutions to a system of two linear equations in two variables as points of intersection of their graphs because points of intersection satisfy both equations simultaneously. |
Pennsylvania Core Standards:
M08.B-E.3.1.4
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Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations. Solve simple cases by inspection. |
Pennsylvania Core Standards:
M08.B-E.3.1.5
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Solve real-world and mathematical problems leading to two linear equations in two variables. |
Florida - Benchmarks for Excellent Student Thinking:
MA.8.AR.2.3
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Given an equation in the form of x2=- and x3=q, where p is a whole number and q is an integer, determine the real solutions. |
Florida - Benchmarks for Excellent Student Thinking:
MA.8.AR.4.1
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Given a system of two linear equations and a specified set of possible solutions, determine which ordered pairs satisfy the system of linear equations. |
Florida - Benchmarks for Excellent Student Thinking:
MA.8.AR.4.2
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Given a system of two linear equations represented graphically on the same coordinate plane, determine whether there is one solution, no solution or infinitely many solutions. |
Florida - Benchmarks for Excellent Student Thinking:
MA.8.AR.4.3
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Given a mathematical or real-world context, solve systems of two linear equations by graphing. |
Georgia Standards of Excellence (GSE):
8.PAR.3.1
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Interpret expressions and parts of an
expression, in context, by utilizing formulas
or expressions with multiple terms and/or
factors. |
Georgia Standards of Excellence (GSE):
8.FGR.7.1
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Interpret and solve relevant
mathematical problems leading to
two linear equations in two
variables. |
Georgia Standards of Excellence (GSE):
8.FGR.7.2
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Show and explain that solutions to
a system of two linear equations
in two variables correspond to
points of intersection of their
graphs, because the points of intersection satisfy both equations
simultaneously. |
Georgia Standards of Excellence (GSE):
8.FGR.7.3
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Approximate solutions of two
linear equations in two variables
by graphing the equations and
solving simple cases by inspection. |
Georgia Standards of Excellence (GSE):
8.FGR.7.4
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Analyze and solve systems of two
linear equations in two variables
algebraically to find exact
solutions. |
Alabama Course of Study Standards:
12.a
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Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of
intersection on their graphs because points of intersection satisfy both equations simultaneously. |
Arizona Academic Standards:
8.EE.C.8a
Common Core State Standards:
Math.8.EE.8a or 8.EE.C.8.A
Kentucky Academic Standards (KAS):
8.EE.8.a
Mississippi College- and Career-Readiness Standards:
8.EE.8a
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Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. |
Georgia Standards of Excellence (GSE):
8.FGR.7.2
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Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of intersection satisfy both equations simultaneously. |
North Carolina - Standard Course of Study:
8.EE.8
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Analyze and solve a system of two linear equations in two variables in slope-intercept form.- Understand that solutions to a system of two linear equations correspond to the points of intersection of their graphs because the point of intersection satisfies both equations simultaneously.
- Solve real-world and mathematical problems leading to systems of linear equations by graphing the equations. Solve simple cases by inspection.
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New York State Next Generation Learning Standards:
8.EE.8.a
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Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Recognize when the system has one solution, no solution, or infinitely many solutions. |
Alabama Course of Study Standards:
12.b
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Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or
infinitely many solutions) when applied to real-world and mathematical problems. |
Arizona Academic Standards:
8.EE.C.8b
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Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations including cases of no solution and infinite number of solutions. Solve simple cases by inspection. |
Common Core State Standards:
Math.8.EE.8b or 8.EE.C.8.B
Kentucky Academic Standards (KAS):
8.EE.8.b
Mississippi College- and Career-Readiness Standards:
8.EE.8b
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Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. |
Georgia Standards of Excellence (GSE):
8.FGR.7.3
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Approximate solutions of two linear equations in two variables by graphing the equations and solving simple cases by inspection. |
Massachusetts Curriculum Frameworks:
8.EE.C.8.b
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Solve systems of two linear equations in two variables algebraically (using substitution and elimination strategies), and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. |
New York State Next Generation Learning Standards:
8.EE.8.b
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Solve systems of two linear equations in two variables with integer coefficients: graphically, numerically using a table, and algebraically. Solve simple cases by inspection.
e.g., 3x + y = 5 and 3x + y = 6 have no solution because 3x + y cannot simultaneously be 5 and 6.
Notes:- Solving systems algebraically will be limited to at least one equation containing at least one variable whose coefficient is 1. Algebraic solution methods include elimination and substitution.
- This standard is a fluency expectation for grade 8.
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Ohio's Learning Standards:
8.EE.8.b
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Use graphs to find or estimate the solution to a pair of two simultaneous linear equations in two variables. Equations should include all three solution types: one solution, no solution, and infinitely many solutions. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. |
Wisconsin Academic Standards:
8.EE.C.8.b
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Solve systems of two linear equations in two variables by graphing and analyzing tables. Solve simple cases represented in algebraic symbols by inspection.
For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. |
Arizona Academic Standards:
8.EE.C.8c
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Solve mathematical problems and problems in real-world context leading to two linear equations in two variables. |
Common Core State Standards:
Math.8.EE.8c or 8.EE.C.8.C
Kentucky Academic Standards (KAS):
8.EE.8.c
Mississippi College- and Career-Readiness Standards:
8.EE.8c
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Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two
pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. |
Georgia Standards of Excellence (GSE):
8.FGR.7.4
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Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions. |
New York State Next Generation Learning Standards:
8.EE.8.c
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Solve real-world and mathematical problems involving systems of two linear equations in two variables with integer coefficients.
Note: Solving systems algebraically will be limited to at least one equation containing at least one variable whose coefficient is 1. |
Ohio's Learning Standards:
8.EE.8.c
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Solve real-world and mathematical problems leading to pairs of linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. (Limit solutions to those that can be addressed by graphing.) |
Wisconsin Academic Standards:
8.EE.C.8.c
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Solve real-world and mathematical problems leading to two linear equations in two variables.
For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. |
Arkansas Academic Standards:
8.ALG.3
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Analyze and solve systems of linear equations in the form y = mx + b in real-world or mathematical contexts, graphically and algebraically. |
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8th Grade Math - Solve Systems of Linear Equations Lesson