Pair of Linear Equations in Two Variables

Topics in this chapter

• Setting Up Linear Equations
• Graphical Solutions and Intersections
• Algebraic Solution Methods
• Consistency and Number of Solutions
• Linear Equation Word Problems
• Coordinate and Area Applications

Cheat sheet

Practice questions

1. Question 1Q-CD1CFC

   For what value of $k$ do the equations $3x - y = 5$ and $6x - 2y = k$ represent coincident lines?

   1. A.5
   2. B.10
   3. C.-10
   4. D.Any real number except 10
   See the answer and solution
2. Question 2Q-F6197D

   The pair of linear equations $x + 2y = 3$ and $5x + 10y = 15$ has:

   1. A.A unique solution
   2. B.No solution
   3. C.Infinitely many solutions
   4. D.Exactly two solutions
   See the answer and solution
3. Question 3Q-C125D6

   If a pair of linear equations is consistent, then the lines will be:

   1. A.Always parallel
   2. B.Always intersecting
   3. C.Intersecting or coincident
   4. D.Always coincident
   See the answer and solution
4. Question 4Q-1D9427

   Solve the following pair of linear equations using the substitution method: $2x + y = 7$ and $4x - 3y = 1$.

   See the answer and solution
5. Question 5Q-569C5D

   Find the value of $k$ for which the system of equations $kx + 3y = k - 3$ and $12x + ky = k$ has no solution.

   1. A.6
   2. B.-6
   3. C.0
   4. D.3
   See the answer and solution