Mathematics
Grade 11
15 min
Solve a non-linear system of equations
Solve a non-linear system of equations
What you'll learn
- Solve division problems with a divisor of 5, using manipulatives or drawings, with 80% accuracy.
- Identify the number of groups when dividing a set of objects into groups of 5 in at least 4 out of 5 attempts.
- Explain, in their own words, how division by 5 is related to repeated subtraction using examples.
- Apply knowledge of division by 5 to solve simple word problems involving sharing equally among 5 friends or objects, with at least 3 out of 4 correct answers.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify a system of equations as linear or non-linear.
Solve a non-linear system of equations using the substitution method.
Solve a non-linear system of equations using the elimination method.
Interpret the solutions of a non-linear system graphically as the points of intersection of their curves.
Solve systems involving a line and a conic section (e.g., parabola, circle).
Solve systems involving two conic sections (e.g., two circles, a circle and a hyperbola).
Determine the number of possible real solutions for a given non-linear system.
Ever wonder how GPS pinpoints your location? 🛰️ It involves solving a system of equations where signals from satellites form intersecting spheres!
In this tutorial, you'll move beyond straight lines and learn h...
2
Key Concepts & Vocabulary
TermDefinitionExample
Non-Linear System of EquationsA set of two or more equations, where at least one equation's graph is not a straight line. The solution is the set of ordered pairs (x, y) that satisfies all equations in the system.The system containing y = 2x + 3 (a line) and x² + y² = 9 (a circle) is a non-linear system.
Point of IntersectionThe graphical representation of a solution to a system. It is the coordinate point where the graphs of the equations cross each other.The graphs of y = x² and y = x + 2 intersect at the points (-1, 1) and (2, 4), which are the two solutions to the system.
Substitution MethodAn algebraic technique where you solve one equation for a single variable and then substitute that expression into the other equation to eliminate one variable.For the sy...
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Core Formulas
The Substitution Method Steps
1. Isolate a variable in one equation.
2. Substitute the resulting expression into the other equation.
3. Solve the new equation.
4. Back-substitute the result(s) into the isolated equation to find the corresponding values of the other variable.
This is the most reliable method, especially when one of the equations is linear or can be easily solved for a variable like y or x².
The Elimination Method Steps
1. Align like terms in both equations.
2. Multiply one or both equations by constants to make the coefficients of one variable opposites.
3. Add the equations to eliminate that variable.
4. Solve the resulting equation and back-substitute.
This method is most efficient when both equations have terms with the same variable and power, such...
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Challenging
For what positive value of 'k' will the system y = x² and x² + (y-k)² = 4 have exactly two real solutions?
A.-1
B.0
C.1
D.-2
Challenging
Find the points of intersection for the system xy = 8 and x + y = 6.
A.(2, 4) and (4, 2)
B.(-2, -4) and (-4, -2)
C.(2, 4) and (-2, -4)
D.(8, -2) and (-2, 8)
Challenging
How many points of intersection do the circles (x - 3)² + y² = 4 and (x + 3)² + y² = 4 have?
A.4
B.2
C.1
D.0
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Frequently asked questions
What grade level is "Solve a non-linear system of equations"?
Solve a non-linear system of equations is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Solve a non-linear system of equations?
You'll be able to: Solve division problems with a divisor of 5, using manipulatives or drawings, with 80% accuracy; Identify the number of groups when dividing a set of objects into groups of 5 in at least 4 out of 5 attempts; Explain, in their….
Is "Solve a non-linear system of equations" 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 non-linear system of equations?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.