Curriculum / Math / 8th Grade / Unit 6: Systems of Linear Equations / Lesson 5
Math
Unit 6
8th Grade
Lesson 5 of 11
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Solve systems of linear equations using substitution when one equation is already solved for a variable.
The core standards covered in this lesson
8.EE.C.8.B — 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.
The foundational standards covered in this lesson
8.EE.C.7 — Solve linear equations in one variable.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
One equation is shown below:
$${3x+y=11}$$
a. If you are given that $${y=-1}$$, can you find the value of $$x$$?
b. If you are given that $$y=x-1$$, can you find the value of $$x$$?
Solve the system below using substitution. Write your final answer as a coordinate point.
$${2x-y=16 }$$
$${y=14x+20}$$
In each system below, circle the expression that you will substitute and draw an arrow to the appropriate variable and equation you will substitute it in for. There may be more than one approach for a system. You do not need to solve the systems.
a. $$x=2y+4$$
$$4y-8=x$$
b. $$y=-x$$
$$5x+5y=10$$
c. $$-3x+9=4y$$
$$x=y-3$$
d. $$\frac{1}{2}x=2y+4$$
$$y=4x-1$$
e. $$y=3x+2$$
$$y=-3x+1$$
f. $$x=y$$
$$\frac{4}{5}x-6y=15$$
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Solve the system using substitution. Write your answer as a coordinate point.
$${x=2y+4 }$$ $${4y-8=x}$$
An example response to the Target Task at the level of detail expected of the students.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 4
Lesson 6
Topic A: Analyze & Solve Systems of Equations Graphically
Define a system of linear equations and its solution.
8.EE.C.8.A
Solve systems of linear equations by graphing.
8.EE.C.8.A 8.EE.C.8.B
Classify systems of linear equations as having a unique solution, no solutions, or infinite solutions.
Solve real-world and mathematical problems by graphing systems of linear equations.
8.EE.C.8.C
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Topic B: Analyze & Solve Systems of Equations Algebraically
8.EE.C.8.B
Solve systems of linear equations using substitution by first solving an equation for a variable.
Solve real-world and mathematical problems using linear systems and substitution.
Solve systems of linear equations using elimination (linear combinations) when there is already a zero pair.
Solve systems of linear equations using elimination (linear combinations) by first creating a zero pair.
Solve real-world and mathematical problems using systems and any method of solution.
8.EE.C.8.B 8.EE.C.8.C
Model and solve real-world problems using systems of equations.
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