A common point solves both equations
Every point on a line satisfies its equation. An intersection lies on both lines and therefore satisfies both equations.
Learning goals
- Generate and verify coordinate pairs for each equation.
- Draw both lines with labelled, consistent scales.
- Read and verify the common solution.
Concept lesson
Coordinates and scale
Plot x first horizontally and y vertically. Label axes, origin and one constant scale per axis.
Graphical solution workflow
Make a value table for each equation, verify at least two points, plot with a consistent scale, draw and label both lines, read their common point, then substitute it in both equations.
Build coordinate tables
For x+2y=6 use (0,3), (2,2), (6,0). For x+y=5 use (0,5), (2,3), (5,0). Substitute each point before plotting.
Read and verify the intersection
The two example lines intersect at (4,1). Check: 4+2(1)=6 and 4+1=5. Hence x=4, y=1 is the common solution.
Plot with error detection
Plot 2x+y=8 and x-y=1. The interactive checker rejects a point that fails its equation and warns if the scale changes along an axis.
Verify both, not one
Test the visually estimated intersection in both original equations. If either equality fails, reread the axes or improve the graph.
Judge graph precision
Explain why a graphical solution can be approximate when the intersection has non-integral coordinates, and why algebraic verification is valuable.
Four-mark graphical answer
Show two value tables, axes and scale, at least two accurate points per line, labelled lines, the intersection and a final ordered-pair answer.
Exit ticket
Solve graphically x+2y=8 and x-y=2. Include tables, labelled scale and both lines, then verify the intersection in both equations.