MA19.8.12

Mathematics (2019) Grade(s): 8

MA19.8.12
Solve systems of two linear equations in two variables by graphing and substitution.

Unpacked Content

Knowledge

Students know:

The properties of operations and equality and their appropriate application.
Graphing techniques for linear equations (using points, using slope-intercept form, using technology).
Substitution techniques for algebraically finding the solution to a system of linear equations.

Skills

Students are able to:

generate a table from an equation.
Graph linear equations.
Identify the ordered pair for the point of intersection.
Explain the meaning of the point of intersection (or lack of intersection point) in context.
Solve a system algebraically using substitution when both equations are written in slope-intercept form or one is written in standard form and the other in slope-intercept form.

Understanding

Students understand that:

any point on a line when substituted into the equation of the line, makes the equation true and therefore, the intersection point of two lines must make both equations true.
Graphs and equations of linear relationships are different representations of the same relationships, but reveal different information useful in solving problems, and allow different solution strategies leading to the same solutions.

Vocabulary

System of linear equations
Point of intersection
One solution
No solution
Infinitely many solutions
Parallel lines
Slope-intercept form of a linear equation
Standard form of a linear equation

Aligned Learning Resources

System of Equations -- Part I Graphing

Solving Systems of Linear Equations -- Part 2 Substitution

Systems of Equations Part 3 -- Solving by Elimination

Graphville Shopping Excursion

Stained Glass Systems

Solving Systems of Equations

Graphing a System of Equations

Using the Substitution Method to Solve Systems of Linear Equations | Algebra 1: Module 5: Topic 7

Calculating Where Lines Intersect

Methods of Solving a System of Linear Equations in Two Variables

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