Mathematics
Grade 4
15 min
Solve a system of equations in three variables using elimination
Solve a system of equations in three variables using elimination
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1
Introduction & Learning Objectives
Learning Objectives
Identify three different 'mystery angles' in a picture puzzle.
Understand that mystery angles can be added together to make a total angle, like 180 or 360 degrees.
Use the 'matching and removing' (elimination) strategy to find the value of one mystery angle.
Substitute the value of a known angle into a clue to help find the value of another.
Solve a complete angle puzzle with three mystery angles.
Check their answers to make sure all the clues in the puzzle are true.
Can you figure out the secret size of each angle shape in our puzzle? 🧩 Let's become angle detectives and crack the code!
Today, we will learn how to solve fun puzzles with three mystery angles. We will use special clues and a strategy called 'elimination'...
2
Key Concepts & Vocabulary
TermDefinitionExample
Mystery Angle (Variable)A shape, like a heart ❤️ or a star ⭐, that stands for an angle whose size in degrees we don't know yet.In our puzzle, a blue triangle 🔺 might be a mystery angle we need to figure out.
Angle Puzzle (System of Equations)A set of picture clues where different groups of mystery angles add up to a total number of degrees.A puzzle might have two clues: Clue 1 is ❤️ + ⭐ = 90 degrees, and Clue 2 is ⭐ + 🟢 = 100 degrees.
Clue (Equation)One line in our angle puzzle that shows a combination of mystery angles and their total.The picture showing 🔺 + 🔺 + 🟦 = 180 is one clue in our puzzle.
Total Angle (Constant)The number that a group of mystery angles adds up to, like 90 degrees (a right angle) or 360 degrees (a full circle).In the clue 🟡 + 🟡...
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Core Formulas
The Difference Rule (Elimination)
(Clue A) - (Clue B) = (Total A) - (Total B)
Use this rule when two clues have a matching part. By finding the difference between the clues, you 'eliminate' the matching parts and can find the value of the part that is different.
The Substitution Rule
If ⭐ = 40, then ⭐ + ❤️ = 90 \rightarrow 40 + ❤️ = 90
Once you know the value of one mystery angle, you can plug that number into other clues. This helps you solve for the rest of the mystery angles in the puzzle.
4 more steps in this tutorial
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Challenging
A puzzle is described in words: 'A star angle (⭐) and a moon angle (🌙) together make a right angle (90 degrees). A star, a moon, and a sun (☀️) together make a straight line (180 degrees). The sun and the star together make 130 degrees.' What is the value of the moon angle (🌙)?
A.🌙 = 40
B.🌙 = 50
C.🌙 = 90
D.🌙 = 60
Challenging
Solve this puzzle to find the value of the diamond (🔷).
Clue 1: 🔴 + 🔷 = 225
Clue 2: 🔴 + ⭐ = 195
Clue 3: 🔴 + 🔷 + ⭐ = 360
A.🔷 = 165
B.🔷 = 140
C.🔷 = 135
D.🔷 = 125
Challenging
Study the puzzle:
Clue 1: 🔺 + 🟦 = 110
Clue 2: 🟦 + 🟢 = 150
Clue 3: 🔺 + 🟦 + 🟢 = 190
Based on the puzzle, which statement is true?
A.The triangle (🔺) is 80 degrees
B.The green circle (🟢) is larger than the triangle (🔺)
C.The square (🟦) is the smallest angle
D.The triangle (🔺) and the green circle (🟢) are the same size
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