What you’ll learn
Choose graph/substitution/elimination.
Key idea
One point on one line does not justify a system solution; both relationships are required.
Graphing uses both constraints; another algebraic method can be valid, but a one-line or axis-swapped argument is not.
Worked example
Enter the exact value or ordered values in the format requested below.
Choose a justified method from the available exact graph: repeated R/B marks define full straight lines, C their crossing; 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).
- The fully labeled graph has a unique exact crossing at (0,1), so graphing supplies a direct method using the given representation.
- Check both equations at that crossing: 2(0)+1=1 and -4(0)+1=1. Two points per line including the crossing justify the construction.
Answer: Graphing
Quick Check
Relate the graph used in 'Choose graph/substitution/elimination' to an equation, table, transformation, or verbal description.
For R: y=2x+4; B: y=-3x-1, connect this exact labeled graph to a method AND complete solution. C is shared, 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).