Checkpoint: the two algebra roads

For 2x + 3y = 12 and x − y = 1, what starts the substitution road?

• Add the two equations together
• Put `2x + 3y` in place of 12 in the second equation
• Rearrange `x − y = 1` to say `x = y + 1`

To remove y from 3x + 2y = 370 and x + y = 140, what scaling comes first?

• No scaling. Subtract straight away
• Multiply the second equation by 2, giving `2x + 2y = 280`
• Multiply the first equation by 2, giving `6x + 4y = 740`

Two learners solve one pair by different roads. Their answers differ. What follows?

• A slip is hiding somewhere. Both original equations will show it
• The pair has two different solutions
• Substitution is unreliable

Eliminating y from a pair ends at 0 = 0. What is the verdict?

• Both equations draw one line. Every point of it is a solution
• No solution
• Exactly one solution