Mathematics
Grade 11
15 min
Solve multi-variable equations
Solve multi-variable equations
What you'll learn
- Identify the value of a digit in a 3-digit number (ones, tens, hundreds) with 80% accuracy on a worksheet.
- Explain how the position of a digit affects its value in a number up to 999, using examples like 'In 325, the 2 means 20' in a written sentence.
- Solve problems where they have to find the number that matches clues about the value of its digits (e.g., 'I have 3 hundreds, 5 tens, and 2 ones. What number am I?') and correctly answer 3 out of 4 problems.
- Apply understanding of place value by writing a 3-digit number that meets specific criteria (e.g., 'Write a number with a 5 in the tens place and a 2 in the hundreds place.') with 100% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Isolate a specific variable in a complex literal equation involving exponents, roots, and fractions.
Solve systems of two linear equations with two variables using both the substitution and elimination methods.
Solve systems of three linear equations with three variables using systematic elimination.
Solve non-linear systems of equations, specifically those involving a line and a conic section (e.g., a parabola or circle).
Interpret the results of a system to determine if it has one solution, no solution, or infinitely many solutions.
Translate a real-world word problem into a system of multi-variable equations and solve it.
Ever wondered how GPS pinpoints your exact location using signals from multiple satellites? 🛰️ It's all done by solving a syste...
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Key Concepts & Vocabulary
TermDefinitionExample
Multi-variable Equation (Literal Equation)An equation that contains two or more variables. Often, the goal is to express one variable in terms of the others.The formula for the area of a trapezoid, A = (1/2)h(b_1 + b_2), is a multi-variable equation with variables A, h, b_1, and b_2.
System of EquationsA collection of two or more equations that share the same set of variables.The set of equations { y = 2x + 1, y = -x + 4 } is a system of two equations with two variables, x and y.
Solution to a SystemA set of values for the variables that makes all equations in the system true at the same time. For a 2D system, this is the point of intersection of the graphs.For the system { y = 2x + 1, y = -x + 4 }, the solution is (x=1, y=3) because 3 = 2(1) + 1 and 3 = -(1) + 4 are...
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Core Formulas
The Substitution Method
1. Solve one equation for one variable. 2. Substitute this expression into the other equation. 3. Solve the resulting equation. 4. Back-substitute to find the other variable(s).
This method is most efficient when one of the equations can be easily solved for a variable (e.g., y = ... or x = ...).
The Elimination Method
1. Align equations by variable. 2. Multiply one or both equations by constants so that the coefficients of one variable are opposites. 3. Add the equations together to eliminate that variable. 4. Solve for the remaining variable and back-substitute.
This method is ideal when variables are already aligned in standard form (Ax + By = C) and coefficients are the same, opposite, or easy multiples of each other.
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Easy
Which of the following best defines a 'system of equations'?
A.single equation that contains more than one variable.
B.collection of two or more equations that share the same set of variables.
C.The process of isolating a variable in a formula.
D.non-linear equation, such as the equation of a circle or parabola.
Easy
Graphically, what does an inconsistent system of two linear equations in two variables look like?
A.Two lines that intersect at a single point.
B.Two lines that are identical and overlap completely.
C.Two parallel lines that never intersect.
D.line and a parabola that intersect at two points.
Easy
Given the equation for the area of a trapezoid, A = (1/2)h(b₁ + b₂), solve for the variable h.
A.h = 2A / (b₁ + b₂)
B.h = A / (2(b₁ + b₂))
C.h = A(b₁ + b₂) / 2
D.h = 2A - b₁ - b₂
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Frequently asked questions
What grade level is "Solve multi-variable equations"?
Solve multi-variable equations is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Solve multi-variable equations?
You'll be able to: Identify the value of a digit in a 3-digit number (ones, tens, hundreds) with 80% accuracy on a worksheet; Explain how the position of a digit affects its value in a number up to 999, using examples like 'In 325, the 2 means 20'….
Is "Solve multi-variable 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 multi-variable equations?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.