What you’ll learn
Solve linear systems graphically.
Key idea
For construction use two distinct points per label and preserve horizontal/vertical order.
A point on only one line, swapped coordinates or swapped line labels cannot establish the system solution.
Worked example
Enter the exact value or ordered values in the format requested below.
Read the ordered-pair solution of the two straight lines below; connect repeated marks of each label. C belongs to both. x horizontal, y vertical.
Marked coordinates: B=(-2, 9); B=(-1, 5); R=(2, 5); R=(1, 3); C=(0, 1); R=(-1, -1); R=(-2, -3); B=(1, -3); B=(2, -7).
- R rises 2 per unit right from intercept 1; B changes -4 per unit right from intercept 1.
- Both traces share C=(0,1); substitution gives 2(0)+1=1 and -4(0)+1=1. Their different slopes give just one intersection.
Answer: (0,1)
Quick Check
Relate the graph used in 'Solve linear systems graphically' to an equation, table, transformation, or verbal description.
Connect the labeled straight graph to BOTH equations using slopes and intercepts. C marks the crossing; x horizontal, y vertical.
Marked coordinates: B=(-3, 8); R=(1, 6); B=(-2, 5); R=(0, 4); C=(-1, 2); R=(-2, 0); B=(0, -1); R=(-3, -2); B=(1, -4).