8th Grade, CC3, Unit 5
Systems of Equations
In Section 5.1, students will continue to solve equations (review of Chapter 3). They will study how to solve multi-variable equations for one of the variables. Students will also learn how to solve equations that contain fractions.
In Section 5.2, students will start by examining word problems in which two amounts are compared. They will use their knowledge of graphs and rules to write equations for word problems. Then, using the equation mat, students will solve a pair of linear equations to determine where two lines cross.
Equal Values Method
Fraction Buster Method
point of intersection
system of equations
y = mx+b form
All Methods & Meanings are available in the textbook. For classroom notes and other handouts, talk to your teacher.
8.EE.7 Solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms until an equivalent equation in the form x = a, a = a, or a = b results.
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
8.EE.8 Analyze and solve pairs of simultaneous linear equations.
a. 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.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
Solve real-world and mathematical problems leading to two linear equations in two variables.