Learn Class 10 Math - Pair of Linear Equations in Two Variables

The linear equations are in the form of ax + by + c = 0. When we see the linear equations, then they are in the form of a straight line. In the above equation, a, b, & c are real numbers, in which a & b are not equal to zero. At the same time, x & y are the two variables. And c is the constant.

Pair of linear equations

When two linear equations are with each other, they are considered a pair of linear equations. In which both x & y terms are different from every equation.

  • First equation: a1x + b1y + c = 0.
  • Second equation: a2x + b2y + c = 0.

Graphical method

There are also some graphical methods to represent the linear equations in two variables. All these methods are discussed below:

  • When two linear equations intersect at a single point, that point is the solution for the particular equations.
  • When the two points coincide, there are infinite solutions to the linear equation on that point.
  • And when both lines move parallel to each other, there is no solution for such an equation. Further, this pair is known as the inconsistent point.

Methods of solving equations

  • Substitution method.
  • Cross multiplication method.
  • Elimination method.

Learning Videos for 10th Grade Math - Pair of Linear Equations in Two Variables

Pair of Linear Equations in Two Variables Sample Questions for Class 10

Question 1

Determine the solutions of x^2 - 14x +49 = 48.
A. - 7 +- 4sqrt3
B. - 7 +- 16sqrt3
C. 7 +- 4sqrt3
D. 7 +- 16sqrt3

Question 2

Solve the system of equations.2x-y+2z=15-x+y+z=33x-y+2z=18
A. (5,3,1)
B. (3,1,5)
C. (-3,5,1)
D. "No Solution"

Question 3

Solve the inequality | x - 2 | - 3 ≥ -2 .
A. x>=1 or x<=3
B. x<=1 or x>=3
C. x<=1 or x>=1
D. None of the above

Question 4

Declare which of the following is the solution to 10x^2 + x -2 = 0.
A. x = - 5, x = -2
B. x = - 1/2, x = 2/5
C. x = - 2/5, x = 1/2
D. x = 2, x = 5

Question 5

Express the following in simplest radical form using only one radical sign. 9^(1/2)*x^(3/2)*y^(5/4)
A. 9sqrt(x^3y^(5/2))
B. 3sqrt(x^3y^(5))
C. 3sqrt(x^3y^(5/2))
D. sqrt(9x^3y^(5))