Simultaneous equations in shapes

• What do variables represent in problems?

  Unknown numbers
• What does knowing the area of a square block allow you to do?

  Write an equation to find side length
• What is the purpose of using letters like x and y?

  To mark the missing pieces until found
• What is the significance of identifying variables in a problem?

  It helps in solving for unknown measurements
• What are variables compared to in the problem?

  Puzzles with missing pieces
• What are the steps in the elimination method for simultaneous equations?

  1. Align the equations for addition or subtraction
  2. Add or subtract the equations to eliminate a variable
  3. Solve for the remaining variable
  4. Substitute back to find the eliminated variable
• What is the formula for the area of a triangle?

  $A =$$\frac{1}{2} bh$
• What can we write based on given information about a shape?

  Equations showing relationships between measurements
• What is the formula for the area of a rectangle?

  $A =$$bh$
• If the base and height of a triangle are 6 cm and 8 cm respectively, what is its area?

  $24 \text{ cm}^2$
• If the radius of a circle is 5 cm, what is its area?

  $25\pi \text{ cm}^2$
• If the length and width of a rectangle are 5 cm and 4 cm respectively, what is its area?

  $20 \text{ cm}^2$
• What is the second method to solve for variables mentioned?

  Elimination
• If the area of a square is 16, what equation would you write?

  $x^{2} =$$16$
• What is the process of setting up equations based on shape information?

  • Identify known information about the shape
  • Write it down as an equation
  • Use the equation to find missing dimensions
• How does writing down an equation help with shapes?

  It helps find the missing pieces of information
• What are the types of information given and corresponding equations to write?

  • Area, one side: Substitute into area formula
  • Perimeter, one side: Use perimeter formula
  • Area, multiple sides: Multiple area formulas
• How do variables help in solving problems involving shapes?

  They allow us to represent unknown dimensions
• When is the elimination method most effective?

  When expressions align easily for addition or subtraction
• Why can equations be solved together?

  When we have more than one unknown
• In a rectangle, what do the sides represent?

  The missing pieces (variables) to find
• What is the elimination method in solving simultaneous equations?

  Add or subtract equations to eliminate a variable
• How does the substitution method work in solving simultaneous equations?

  One equation is solved for a variable and substituted
• How do the results from substitution and elimination methods compare in solving the equations?

  Both methods yield $x =$$4$ and $y =$$2$
• What is the purpose of solving for variables in a puzzle?

  To find all the missing pieces
• Which letters are commonly used to mark missing pieces?

  x and y
• After finding $x =$$4$, how do you find $y$?


  Substitute $x =$$4$ into $y =$$x - 2$
• What is the first equation given in the image?

  2x + 4y = 8
• Why are variables considered missing pieces?

  They represent unknown values we need to find
• Why is it essential to substitute values back into the original equations?

  To verify that the solution satisfies both equations
• What is the formula for the area of a trapezoid?

  $A =$$\frac{a+b}{2}h$
• What is the first solution given in the image?

  y = 6/2
• What is the result of adding the equations $2x +$$y =$$10$ and $x - y =$$2$ to eliminate $y$?


  $3x =$$12$
• What are equations compared to in the context of shapes?

  Secret notes that connect shape blocks
• What do you get when substituting $y =$$x - 2$ into $2x +$$y =$$10$?


  $3x =$$12$
• What is the first method to solve for variables mentioned?

  Substitution
• What happens when you combine a $+$$y$ block and a $- y$ block?


  They cancel each other out
• What is the first step in the substitution method using the equations $2x +$$y =$$10$ and $x - y =$$2$?


  From $x - y =$$2$, solve for $y$
• What is the third equation given in the image?

  2y = 6
• What is the purpose of checking the solution of simultaneous equations?

  To confirm the solution is correct