Mathematics
Grade 11
15 min
Solve a system of equations using elimination
Solve a system of equations using elimination
What you'll learn
- Identify groups of 4 within a set of objects and write the corresponding division equation with at least 80% accuracy.
- Solve division word problems involving dividing by 4, showing your work with drawings or number sentences, and get the correct answer in at least 3 out of 4 problems.
- Explain what it means to divide by 4 using pictures, words, or objects, demonstrating understanding in a short oral explanation to the teacher or a partner.
- Apply the concept of dividing by 4 to share a collection of items equally among 4 friends, showing the result with a drawing and a division equation.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify when the elimination method is the most efficient strategy for solving a system of linear equations.
Manipulate one or both equations in a system by multiplication to create opposite coefficients for one variable.
Add or subtract linear equations to eliminate one variable and solve for the remaining variable.
Substitute a solved variable's value back into an original equation to find the value of the second variable.
Identify systems with no solution (inconsistent) or infinitely many solutions (dependent) when using the elimination method.
Verify the solution by substituting the ordered pair into both original equations.
Set up and solve a system of linear equations from a real-world word problem using elimination.
Imagine you're an e...
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Key Concepts & Vocabulary
TermDefinitionExample
System of Linear EquationsA set of two or more linear equations that share the same variables. The goal is to find the values of the variables that satisfy all equations in the set simultaneously.The equations 2x + y = 5 and 3x - y = 10 form a system. The solution is the ordered pair (x, y) that makes both statements true.
Elimination MethodAn algebraic technique for solving a system of equations by adding or subtracting the equations to 'eliminate' one of the variables.Given x + y = 10 and x - y = 2, adding the two equations eliminates 'y', resulting in 2x = 12.
CoefficientThe numerical factor multiplied by a variable in an algebraic term.In the term -7y, the coefficient is -7.
Opposite CoefficientsCoefficients of the same variable in two differe...
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Core Formulas
Addition Property of Equality
If A = B and C = D, then A + C = B + D
This is the fundamental principle behind the elimination method. It allows us to add two equations together, combining the left sides and the right sides, to create a new, valid equation.
Multiplication Property of Equality
If A = B, then cA = cB for any non-zero constant c
This rule allows us to multiply an entire equation by a constant to create a new, equivalent equation. We use this to create opposite coefficients for a variable if they don't already exist.
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Challenging
When using the elimination method to solve a system of two linear equations, you arrive at the statement 0 = 12. What does this result imply about the graphs of the two equations?
A.The lines are perpendicular.
B.The lines intersect at a single point.
C.The lines are identical (coincident).
D.The lines are parallel and distinct.
Challenging
For what value of `k` will the system `2x + 3y = 7` and `4x + ky = 14` be a dependent system (have infinitely many solutions)?
A.k = 3
B.k = 7
C.k = 6
D.k = 12
Challenging
For the system `x - 2y = 5` and `-3x + 6y = k` to be inconsistent (have no solution), what must be true about the value of `k`?
A.k = 15
B.k = -15
C.k ≠ 15
D.k ≠ -15
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Frequently asked questions
What grade level is "Solve a system of equations using elimination"?
Solve a system of equations using elimination is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Solve a system of equations using elimination?
You'll be able to: Identify groups of 4 within a set of objects and write the corresponding division equation with at least 80% accuracy; Solve division word problems involving dividing by 4, showing your work with drawings or number sentences….
Is "Solve a system of equations using elimination" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Solve a system of equations using elimination?
This lesson includes 24 practice questions across multiple difficulty levels, each with instant feedback and explanations.