Practice question · True or false
A system of two linear equations in two unknowns can have exactly two solutions.
Hints
- Two straight lines can meet how many times?
- One point, never, or everywhere along the line.
Show the answer
False
Why
False. Two lines meet at one point, are parallel and never meet, or coincide and share infinitely many, there is no configuration giving exactly two. It generalises: a linear system always has one, none, or infinitely many solutions, which is a structural fact about linearity rather than about two dimensions.
Practise Systems of Linear Equations
The app has 5 more questions on this lesson, and keeps your place in the course. Computer Science I is free to start.
More questions on Systems of Linear Equations
- Order the steps of solving 'x + y = 5, 2x + y = 8' by elimination.
- Sort each equation by whether it is linear in x and y.
- A neural network layer is a matrix multiply followed by a non-linear function. Why is the non-linearity…
- The system 'x + y = 4, 2x + 2y = 8' has infinitely many solutions. Select every pair (x, y) that is a…