Two linear equations in two unknowns are two straight lines, and their solution is where the lines meet. This course solves such pairs by graph, substitution and elimination, and turns word problems into equations.
The course follows the NCERT Mathematics chapter Pair of Linear Equations in Two Variables and has 6 lessons. Each lesson explains the ideas with worked examples and ends with practice questions and full answers. The numbers in every example and question are our own, so the lessons can be used alongside the textbook exercises.
- Two Lines: Intersecting, Parallel or Coincident, A pair of linear equations is a pair of lines, and lines meet once, never, or everywhere. The three pictures, what each means for solutions, and the coefficient-ratio test that decides the case without drawing.
- Forming and Classifying Pairs: Practice, Ten questions on turning a situation into a pair of equations, classifying a pair by its coefficients, drawing the lines, and finding the constant that makes a pair parallel or coincident. Full answers.
- The Substitution Method, Express one variable in terms of the other, substitute, solve. Worked through with a whole-number answer, a fractional one, and the two cases where the variable disappears, which tell you the lines are parallel or coincident.
- Substitution: Practice, Ten questions solved by substitution, five plain pairs including one with fractions, then word problems on ages, prices, two-digit numbers and fractions, each with the equations formed first.
- The Elimination Method, Scale the equations so one variable matches, then add or subtract to remove it. When to add and when to subtract, why a fractional answer is not an error, and how both variables vanishing signals a non-unique case.
- Elimination and Word Problems: Practice, Ten questions, five pairs to eliminate, including decimals and fractional answers, then word problems on prices, digits, boats and streams, incomes, and two cars, with every equation formed and every answer checked.
By the end you will be able to:
- Tell from the coefficients whether a pair of lines intersects, is parallel or coincides.
- Solve a pair of linear equations graphically, by substitution and by elimination.
- Form a pair of equations from a word problem and interpret the solution.
- Reduce some non-linear pairs to linear form by substitution.