Curriculum / Math / 9th Grade / Unit 4: Linear Equations, Inequalities and Systems / Lesson 12
Math
Unit 4
9th Grade
Lesson 12 of 14
Jump To
Identify solutions to systems of equations algebraically using elimination. Write systems of equations.
The core standards covered in this lesson
A.REI.C.5 — Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
The foundational standards covered in this lesson
8.EE.C.8 — Analyze and solve pairs of simultaneous linear equations.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Lisa is working with the system of equations $${x+2y=7}$$ and $${2x-5y=5}$$. She multiplies the first equation by $$2$$ and then subtracts the second equation to find $${9y=9}$$, telling her that $${y=1}$$. Lisa then finds that $${x=5}$$. Thinking about this procedure, Lisa wonders:
There are lots of ways I could go about solving this problem. I could add 5 times the first equation and twice the second, or I could multiply the first equation by $$-2$$ and add the second. I seem to find that there is only one solution to the two equations, but I wonder if I will get the same solution if I use a different method?
Does the answer to (1) change if we have a system of two equations in two unknowns with no solutions? What if there are infinitely many solutions?
Solving Two Equations in Two Unknowns, accessed on Oct. 19, 2017, 4:13 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.
Solve the system:
$${\left\{\begin{matrix} \frac{8}{3}x+\frac{1}{3}y=-\frac{16}{3}\\ -x+\frac{1}{3}y=-\frac{5}{3} \end{matrix}\right.}$$
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
Without solving the systems, explain why the following system must have the same solution.
System 1:
$${4x-5y=13 }$$
$${3x+6y=11}$$
System 2:
$${8x-10y=26}$$
$${x-11y=2}$$
Algebra I > Module 1 > Topic C > Lesson 23 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..
Solve the system of equations by writing a new system that eliminates one of the variables.
$${3x+2y=4}$$
$${4x+7y=1}$$
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 11
Lesson 13
Topic A: Properties and Solutions of Two-Variable Linear Equations and Inverse Functions
Identify the solutions and features of a linear equation and when two linear equations have the same solutions.
A.REI.D.10 A.SSE.B.3
Write linear equations given features, points, or graph in standard form, point-slope form, and slope-intercept form.
A.SSE.B.3 F.IF.B.4 F.IF.C.7.A
Determine if a function is linear based on the rate of change of points in the function presented graphically and in a table of values.
F.IF.B.6 F.IF.C.7.A F.IF.C.9 F.LE.A.1.A
Identify inverse functions graphically and from a table of values in contextual and non-contextual situations.
F.BF.B.4.A F.IF.A.1 F.IF.A.2 F.IF.B.5
Find inverse functions algebraically, and model inverse functions from contextual situations.
A.CED.A.4 F.BF.B.4.A F.IF.B.6
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Properties and Solutions of Two-Variable Linear Inequalities
Describe the solutions and features of a linear inequality. Graph linear inequalities.
A.REI.D.12
Write linear inequalities from graphs.
A.CED.A.3 A.REI.D.12
Write linear inequalities from contextual situations.
A.CED.A.3
Topic C: Systems of Equations and Inequalities
Solve a system of linear equations graphically.
A.CED.A.3 A.REI.D.11
Identify solutions to systems of inequalities graphically. Write systems of inequalities from graphs and word problems.
Solve linear systems of equations of two variables by substitution.
A.CED.A.3 A.REI.C.5 A.REI.C.6 N.Q.A.2
A.REI.C.5
Identify solutions to systems of equations using any method. Write systems of equations.
A.REI.A.1 A.REI.C.6 A.SSE.B.3
Identify solutions to systems of equations with three variables.
A.REI.C.6
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
Access rigorous, relevant, and adaptable math lesson plans for free