What this lesson covers
- Why a question that hands you the candidates is asking you to check, not solve
- Testing a point against both equations, and what a pass actually proves
- Reading "this equation cleared everything" as information instead of failure
- Stopping the moment a point fails one line
- The reverse version: given the point, find the missing coefficient
Questions worked in the video
- 0:172x + y = 11 and x - 3y = -5. Which ordered pair is the solution?
- 1:28If (3, 2) is a solution of 4x - ky = 6, what is k?
- 2:033x - y = 8 and x + 2y = 5. Which ordered pair is the solution?
Chapters
- 0:00Four points, one system
- 0:17The setup
- 0:37Every choice clears the first line
- 1:28One failure is enough
- 2:03Your turn
- 2:43Three ways this goes wrong
- 3:03Both lines, checked
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:17The setup
Here is a system of two linear equations, and four ordered pairs underneath it. Exactly one of them is the solution. The instinct is to solve the system. Do not. You already have the four candidates, so test them instead.
0:37Every choice clears the first line
A point is the solution only if it makes both equations true. Start with choice A, two and seven. Two times two is four, plus seven is eleven. Eleven is what the first equation wanted, so that one checks. Now run the other three through the same equation. Four and three gives eleven. Seven and negative three gives eleven. Five and one gives eleven. Every single choice sits on the first line. That pass eliminated nothing. Which means the first equation was never the deciding one. Switch to the second. Two minus twenty one is negative nineteen. Seven plus nine is sixteen. Five minus three is two. Only four and three lands on negative five. Answer B.
1:28One failure is enough
That is the habit worth keeping. If one equation clears every choice, that is information, not a dead end. Move to the other equation right away. And the moment a point fails one line, stop checking it. One failure is already enough. Same skill, turned around. They tell you three and two is a solution of four x minus k y equals six, and they want k. Substitute. Twelve minus two k is six, so k is three. You are still testing a point, not solving a system.
2:03Your turn
Your turn. Three x minus y is eight. x plus two y is five. Which ordered pair is the solution? Ten seconds. All four sit on the first line again, so that pass tells you nothing. Go straight to the second. One minus ten is negative nine. Four plus eight is twelve. Two minus four is negative two. Three plus two is five. Answer C, three and one.
2:43Three ways this goes wrong
Three ways this goes wrong. One, stopping after the first equation when every choice cleared it. Two, feeding the pair in backwards, which throws away the right answer. Three, solving the whole system when the answer was already sitting in the choices.
3:03Both lines, checked
Test, do not solve. And one failure is enough.
Read the written version: the Systems of two linear equations strategy guide, then try 25 hard Systems of two linear equations questions with full explanations. Both are free, no account needed.