2. Which of the following is a linear equation in one variable?
a) 2x + 1 = y - 3
b) 2t - 1 = 2t + 5
c) 2x - 1 = x
2
d) x
2
- x + 1 = 0
3. Which of the following numbers is a solution for the equation 2(x + 3) = 18?
a) 5 b) 6 c) 13 d) 21
4. The value of x which satisfies the equation 2x - (4 - x) = 5 - x is
a) 4.5 b) 3 c) 2.25 d) 0.5
5. The equation x - 4y= 5 has
a) no solution b) unique solution
c) two solutions d) infinitely many solutions
4.2 SOLUTIONS OF PAIRS OF LINEAR EQUATIONS IN TWO VARIABLES
In the introductory example of notebooks and pens, how many equations did we have?
We had two equations or a pair of linear equations in two variables. What do we mean by the
solution for a pair of linear equations?
A pair of values of the variables x and y which together satisfy each one of the equations
is called a solution for a pair of linear equations.
4.2.1 GRAPHICAL METHOD OF FINDING SOLUTION OF A PAIR OF LINEAR EQUATIONS
What will be the number of solutions for a pair of linear equations in two variables? Is the
number of solutions infinite or unique or none?
In an earlier section, we used the model method for solving the pair of linear equations.
Now we will use graphs to solve the equations.
Let: a1
x + b1
y + c
1
= 0, (a1
2
+ b1
2 ¹ 0) and a2
x + b2
y + c
2
= 0; (a2
2
+ b2
2 ¹ 0) form a pair
of linear equation in two variables.
The graph of a linear equation in two variables is a straight line. Ordered pairs of real
numbers (x, y) representing points on the line are solutions of the equation and ordered pairs of
real numbers (x, y) that do not represent points on the line are not solutions.
If we have two lines in the same plane, what can be the possible relations between them?