Algebraic solution by cross-multiplication
Cross-multiplication is a method used to solve a pair of linear equations written in the form a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0.
Practice This ConceptMain explanation
Teacher explanation
This method uses ratios formed from the coefficients and constants to directly write the values of x and y. It is especially useful when the pair is already in standard form. Students should understand the formula and apply the signs carefully because one wrong sign changes the answer.
Example
For 2x + 3y - 7 = 0 and 3x - 2y - 4 = 0, the cross-multiplication formula can be used to find x and y.
Simple analogy
Standard form first, then cross carefully.
Common confusion
Students often place the coefficients in the wrong positions in the formula or miss the minus signs in the numerators.
Exam tip
Write the coefficients neatly first and keep the standard form consistent before applying the formula.
Answer writing and exam use
1-mark use
Write the exact meaning of algebraic solution by cross-multiplication in one clean line.
2-mark use
Define algebraic solution by cross-multiplication and add one example or condition.
3-mark use
Explain algebraic solution by cross-multiplication, show the method or example, and mention the common mistake.
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