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IGCSEMathsEdexcelMaths A (Modular)Higher Unit 1FlashcardsAlgebraSolving Linear Equations

Solving Linear Equations (Edexcel IGCSE Maths A (Modular))

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  • FrontSolving Linear Equations

    What is the greatest power of x in a linear equation?

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  • What is the greatest power of x in a linear equation?

    The greatest power of x in a linear equation is 1.

    There is no term in x2 or any higher power.

  • What does 'isolate the variable' mean?

    Isolate the variable means to get the variable term, e.g. x, by itself on one side of the equation.

  • What are inverse operations?

    Inverse operations are the opposite operations to what has already happened to the variable.

    E.g. In the expression 4 x, x is being multiplied by 4.
    The inverse operation is to divide by 4.

    Examples of inverse operations are:

    • Add and subtract

    • Multiply and divide

    • Square and take the square root

  • True or False?

    To solve a linear equation, e.g. 3 x plus 4 equals 13, you need to isolate the variable by carrying out inverse operations to both sides.

    True.

    To solve a linear equation, you need to isolate the variable, (get the letter on its own), by carrying out inverse operations to both sides.

    E.g.

    3 x plus 4 equals 13 table row cell negative 4 end cell cell space space space space space space space space space space space space space space space space space space space space minus 4 end cell end table 3 x equals 9 divided by 3 space space space space space space space space space space space space space space space space space space space space space divided by 3 x equals 3

  • What is the order of inverse operations to solve a linear equation of the form a x plus b equals c to find x.

    To solve a linear equation of the form a x plus b equals c:

    • First subtract b from both sides

    • Then divide both sides by a

  • True or False?

    If a linear equation contains the unknown variable on both sides, you should first collect the variable terms on one side.

    E.g. 8 x plus 7 equals 2 x plus 11.

    True.

    If a linear equation contains the unknown variable on both sides, you should first collect the variable terms on one side.

    E.g.

    table row cell 8 x plus 7 end cell equals cell 2 x plus 11 end cell row cell 6 x plus 7 end cell equals 11 end table

  • What is the first step to solve a linear equation with brackets?

    E.g. 4 open parentheses x plus 6 close parentheses equals 32.

    The first step to solve a linear equation with brackets is to expand the brackets (on both sides if necessary).

    E.g.

    table row cell 4 open parentheses x plus 6 close parentheses end cell equals 32 row cell 4 x plus 24 end cell equals 32 end table

  • What is the first step to solve a linear equation with fractions?

    E.g. fraction numerator x plus 9 over denominator 2 end fraction equals fraction numerator 3 x minus 1 over denominator 4 end fraction.

    The first step to solve a linear equation with fractions is to remove the fractions by multiplying both sides by the denominators.

    E.g.

    table row cell fraction numerator x plus 9 over denominator 2 end fraction end cell equals cell fraction numerator 3 x minus 1 over denominator 4 end fraction end cell row cell 4 open parentheses x plus 9 close parentheses end cell equals cell 2 open parentheses 3 x minus 1 close parentheses end cell row blank blank blank end table

  • After solving a linear equation, how can you check your answer to see if it is correct?

    After solving a linear equation, you should substitute your answer back into the equation to check if it is correct.

    This is a quick way to spot if you have made any mistakes.

  • Use algebra to represent double the amount of a quantity, given that x is the initial quantity.

    Double the amount of a quantity x can be written as 2 x.

  • Use algebra to represent half the amount of a quantity, given that x is the initial quantity.

    Half the amount of a quantity x can be written as 1 half x or x over 2 or 0.5 x.

  • Use algebra to represent five more than a quantity, given that x is the initial quantity.

    Five more than a quantity x can be written as x plus 5.

    This is not the same as 5 x.

  • Use algebra to represent ten lots of a quantity, given that x is the initial quantity.

    Ten lots of a quantity x can be written as 10 x.

    This is not the same as x plus 10.

  • True or False?

    If my sister is 2 years younger than me, then x is my age and x minus 2 is her age.

    True.

    If my sister is 2 years younger than me, then x is my age and x minus 2 is her age.

    It is also true to say that y plus 2 is my age and y is her age.

  • Three bags contain x, x plus 5 and x plus 10 marbles each.

    If there are 75 marbles in total, explain how to form an equation.

    Three bags contain x, x plus 5 and x plus 10 marbles each.

    If there are 75 marbles in total, then an equation can be formed by adding all the quantities up and setting them equal to 75.

    This gives x plus open parentheses x plus 5 close parentheses plus open parentheses x plus 10 close parentheses equals 75.

    Examiners want to see this full equation (before simplifying or solving).

Previous:Algebraic FractionsNext:Solving Quadratic Equations

    1. Topic 1

      Number Toolkit

    2. Topic 2

      Set Notation & Venn Diagrams

    3. Topic 3

      Powers & Roots

    4. Topic 4

      Fractions

    5. Topic 5

      Fractions, Decimals & Percentages

    6. Topic 6

      Rounding, Estimation & Bounds

    7. Topic 7

      Surds

    8. Topic 8

      Using a Calculator

    9. Topic 9

      Exchange Rates & Best Buys

    1. Topic 1

      Algebra Toolkit

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding Brackets

    4. Topic 4

      Factorising

    5. Topic 5

      Completing the Square

    6. Topic 6

      Algebraic Fractions

    7. Topic 7

      Solving Linear Equations

    8. Topic 8

      Solving Quadratic Equations

    1. Topic 1

      Coordinate Geometry

    2. Topic 2

      Linear Graphs y = mx + c

    3. Topic 3

      Graphs of Functions

    4. Topic 4

      Real-Life Graphs

    1. Topic 1

      Standard & Compound Units

    2. Topic 2

      Area & Perimeter

    3. Topic 3

      Circles, Arcs & Sectors

    4. Topic 4

      Properties of 3D Shapes

    1. Topic 1

      Right-Angled Triangles: Pythagoras & Trigonometry

    2. Topic 2

      Sine, Cosine Rule & Area of Triangles

    3. Topic 3

      3D Pythagoras & Trigonometry

    1. Topic 1

      Histograms

    2. Topic 2

      Probability Toolkit

    3. Topic 3

      Probability Diagrams: Venn & Tree Diagrams

    4. Topic 4

      Combined & Conditional Probability