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SHS Core Mathematics · Year 2

Equations and Inequalities practice questions

Solving simultaneous linear equations in two variables using the elimination, substitution and graphical methods, and applying them to real-life problems.

25 questions in this topic: 6 recall, 11 applying skills and concepts and 8 strategic thinking. Every one carries a written explanation.

Sample questions

5 of 25 questions in this topic. Sign up to answer them and see the explanations.

  1. Question 1Recall

    In the graphical method for solving simultaneous equations, each linear equation is first rewritten in the form

    • ay = mx + c, so its gradient and y-intercept can be identified for plotting
    • bax + by = 0 only
    • cx = constant
    • da quadratic in x
  2. Question 2Strategic thinking

    Solving 2x + y = 7 and 3x − y = 4 by substitution: rearranging the first equation gives y = 7 − 2x. Substituting into the second gives 3x − (7 − 2x) = 4, which simplifies to 5x − 7 = 4, so x equals

    • a11/5
    • b7/5
    • c1
    • d4/5
  3. Question 3Skills & concepts

    For the line x + y = 6, rewritten as y = −x + 6, the gradient is negative because

    • athe coefficient of x, −1, is negative
    • bthe y-intercept, 6, is positive
    • cx and y are both positive variables
    • dthe line passes through the origin
  4. Question 4Skills & concepts

    A farmer sells 2 bags of maize and 1 bag of soybeans for GH¢150, and 1 bag of maize alone costs GH¢40. Using x = cost of maize and y = cost of soybeans, the equations are 2x + y = 150 and x = 40. Substituting gives 2(40) + y = 150, so y (cost of soybeans) is

    • aGH¢70
    • bGH¢80
    • cGH¢150
    • dGH¢40
  5. Question 5Skills & concepts

    Solving 2x + 3y = 12 and 4x − 3y = 6 by adding the equations (since the y-coefficients have opposite signs) gives 6x = 18, so x equals

    • a3
    • b18
    • c6
    • d2

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