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 Construct and solve linear equations Simultaneous equations with a difference J1: Fishy Equations Work out the weight of each fish. A fishy introduction to simultaneous equations!     J20: Shape people and simultaneous equations Two or three rows of polygon people are shown (click the '2 rows' or '3 rows' buttons). Two numbers are hidden behind the shape people: one behind the triangle and one behind the circle. What are the hidden numbers? Click on the shape people to show or hide the numbers. Traditional simultaneous equations J21: Simultaneous equations generator Click on the four option buttons to generate new simultaneous equations: 1. Positive answers and coefficients of x and y 2. Positive and negative answers and positive coefficients of x and y 3. Positive answers and positive and negative coefficients of x and y 4. Positive and negative answers and coefficients of x and y   Arithmagons In an arithmagon, the number in a square is the sum of the numbers in the two circles on either side of it. What could the letters be? Find relationships between the letters. There are many possible solutions for the arithmagons. The answer sheet will give one set of solutions. J2: Sum puzzle  Solve simple equations J3: Work out what number each shape represents (positive numbers) J4: Work out what number each shape represents (positive and negative numbers) J5: Work out the value of each letter (positive numbers)   Pyramid equations In each pyramid each number is the sum of the two numbers immediately below. Find the value of n J6: Pyramid 1 positive whole number solutions J7: Pyramid 2 positive and negative whole number solutions J8: Pyramid 3 positive whole number solutions. J9: Pyramid 4 positive and negative whole number solutions J10: Pyramid 5 positive whole number solutions J11: Pyramid 6 positive and negative whole number solution Square equations Work out the value of a and b so that each row and column adds up to the required total. J12: Square equations 1: positive whole number solutions. J13: Square equations 2: positive and negative whole number solutions. type 1 Linear equations J14: Type 1 J15: Type 2 J16: Type 3 J17: Type 4

 Use formulae   Substitute numbers into expressions. J18: Substitute positive numbers J19: Substitute positive and negative numbers

 Simplify or transform algebraic expressions Click on the expressions to hide or show them: in the above example click on 3x or 7 or 28x etc. J22: Multiply out brackets (positive values only) eg (3x +2)(2x + 1) = 6x2 + 10x + 2 factorise the expression 6x2 + 10x + 2 J23: Multiply out brackets (positive and negative values) eg (3x -2)(2x + 1) = 6x2 - x - 2 factorise the expression 6x2 - x - 2 Use these buttons to generate a new expression. Click the '1' button to ensure the coefficient of the x terms is 1. Click the '2' button to have random coefficients of x. The diagram might not fit on the screen, click again if this happens. The diagrams are drawn to scale: can you say what the value of x is? Use these buttons to hide or show the expression or the factorised expression. J24: Solve quadratic equations eg: x2 + 3x - 10 = 0 Click twice under each equation to reveal the solutions.