Curriculum / Math / 8th Grade / Unit 6: Systems of Linear Equations / Lesson 10
Math
Unit 6
8th Grade
Lesson 10 of 11
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Solve real-world and mathematical problems using systems and any method of solution.
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.
8.EE.C.8.C — 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.
The foundational standards covered in this lesson
8.EE.C.7 — Solve linear equations in one variable.
8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
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Lessons 10 and 11 bring the concepts of the unit together. This is a good opportunity for students to focus on targeted concepts or skills where they still need practice or development.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Which method—graphing, substitution, or elimination—would you choose to solve each system below? Explain your answer.
$${y={2\over3}x-6}$$
$${y=-{x\over4}+2}$$
$${1.5x-6.2y=18.3}$$
$${1.5x+6.2y=-4.8}$$
$${x=3(y+1)}$$
$${2x+4y=-7}$$
The sum of two numbers is 361, and the difference between the two numbers is 173. What are the two numbers?
Write a system of equations to represent the information above. Solve it using any method.
Grade 8 Mathematics > Module 4 > Topic D > Lesson 29 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
A type of pasta is made of a blend of quinoa and corn. The pasta company is not disclosing the percentage of each ingredient in the blend, but we know that the quinoa in the blend contains 16.2% protein and the corn in the blend contains 3.5% protein. Overall, each 57-gram serving of pasta contains 4 grams of protein. How much quinoa and how much corn is in one 57-gram serving of the pasta?
Quinoa Pasta 1, accessed on March 12, 2017, 6:53 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
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Small boxes contain Blu-ray disks and large boxes contain one gaming machine. Three boxes of gaming machines and a box of Blu-rays weigh 48 pounds. Three boxes of gaming machines and five boxes of Blu-rays weigh 72 pounds. How much does each box weigh?
A language arts test is worth 100 points. There is a total of 26 questions. There are spelling word questions that are worth 2 points each and vocabulary questions worth 5 points each. How many of each type of question are there?
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Lesson 9
Lesson 11
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
Solve systems of linear equations using substitution when one equation is already solved for a variable.
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.
8.EE.C.8.B 8.EE.C.8.C
Model and solve real-world problems using systems of equations.
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