Mathematics (US) - 0444 CIE

Systems Of Linear Equations In Two Variables

Akopọ

One equation with two unknowns has endless solutions; pair it with a second equation and the answer usually pins down to a single point. Solving a system of two linear equations means finding the one pair of values that satisfies both at once, the exact spot where two lines cross.

In this lesson you will solve systems of two linear equations in two variables using elimination and substitution, the two reliable algebraic methods. You will learn to choose the easier route for each problem and to check your answer in both original equations.

Awọn Afojusun

  1. Solve systems of two linear equations in two variables algebraically and (Extended) graphically.

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Akọ̀wé Ẹ̀kọ́

Many real problems involve two unknowns linked by two conditions: the cost of two kinds of ticket, the speed of a boat and a current, a mix of two ingredients. A system of linear equations captures both conditions and solves them together, which is far more powerful than guessing.

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  1. Solve 2x + y = 8 and x - y = 1. A. (3, 2) B. (2, 3) C. (1, 6) D. (4, 0) Answer: A
  2. Solve y = 2x - 1 and 3x + y = 9. A. (3, 2) B. (2, 3) C. (1, 1) D. (2, 5) Answer: B
  3. To eliminate y from x + y = 5 and x - y = 1, you should: A. Add the equations B. Subtract the equations C. Multiply them D. Square them Answer: A
  4. The solution of a system of two linear equations represents: A. The midpoint of two lines B. Where the two lines cross C. The gradient of a line D. The y-intercept Answer: B
  5. Solve x + y = 7 and x - y = 3. A. (5, 2) B. (2, 5) C. (4, 3) D. (3, 4) Answer: A

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