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Flashcards · Maths · Further Algebra

Simultaneous Equations

16 cards

  1. What are simultaneous equations?

    Two or more equations that must be true at the same time.

  2. What does the point where two graphs cross represent?

    The solution of the simultaneous equations.

  3. When do you subtract the equations in elimination?

    When the terms in one letter are the same in both.

  4. When do you add the equations in elimination?

    When the terms in one letter are opposites.

  5. What do you do if no letter has matching numbers?

    Multiply one or both equations to make a pair match.

  6. What is the first step in the substitution method?

    Get one letter on its own in one equation.

  7. Solve \(x + y = 9\) and \(x - y = 1\).

    \(x = 5\), \(y = 4\).

  8. How should you check your solution?

    Substitute both values into the equation you did not use.

  9. What does it mean if two lines are parallel?

    The equations have no solution.

  10. How do you write a word problem as simultaneous equations?

    Define the letters and write one equation for each statement.

  11. What do you do first with a line and a quadratic (Higher tier)?

    Substitute the line into the quadratic to get a quadratic in \(x\).

  12. How many solutions can a line and a circle have (Higher tier)?

    Two, one or none.

  13. Solve \(y = x^2\) and \(y = x + 6\) (Higher tier).

    \((3, 9)\) and \((-2, 4)\).

  14. Why use brackets when substituting an expression?

    They stop sign errors.

  15. How many pairs of values solve a pair of linear equations?

    One, unless the lines are parallel or the same.

  16. What is the equation of the line through \((0, 1)\) with gradient 1?

    \(y = x + 1\).