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Take 2x + 3y = 12. Here x and y are two rupee amounts. What are they?

This chapter is Linear Equations in Two Variables. One equation has many answers. Two equations can have exactly one.

What you will learn

• Two letters. One equation, two unknowns. A solution is a pair.
• Checking a pair. Put the pair in. Both equations must be true.
• One line, many pairs. Every solution sits on one line.
• Where two lines meet. The point that answers both equations.
• When lines refuse. Three things two lines can do.
• Substitution. Name one letter, then use its name.
• Scale, then subtract. Match one letter's coefficients, then subtract.
• Both roads agree. Two methods, one true answer.
• What the algebra says. What is left decides how many solutions.

Need a quick catch-up?

These earlier ideas help. Revisit any one that feels unsure.

• One point needs two numbers. Order matters.
• Reading a line: steepness is a change per step.
• The number in front of a letter is its coefficient.
• The balance: both sides of an equation name one number.
• Moving a term across the equals sign.
• Putting an answer back in to check it.