The solution of two linear equations is where their lines cross; parallel lines have no solution.
What you will learn
- Read a solution from two lines
- Estimate a non-whole-number solution
- Tell when there is no solution
Where the lines cross
Every point on a line fits its equation.
The one point on both lines fits both equations: that is the solution.
Parallel lines (same gradient, different intercepts) never meet, so there is no solution. If the two equations are the same line, every point is a solution.
A graph gives an estimate when the crossing is between grid lines; algebra gives the exact value.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Where the lines cross
- Try it: Move the lines until they cross
7 practice questions, marked as you go; about 20 minutes in all.
In this unit: Simultaneous equations
Solve two equations at once by elimination, substitution and graphs, form them from problems, and (Higher) solve a linear and a quadratic equation together.