Question

To prepare an assignment on behavior of lines representing a pair of Linear Equations in two Variables and existence of solutions. I will give you brilliant answer​

Answer 1

A single solution of a pair of linear equations in two variables

Consider the following pair of linear equations in two variables,

x – 2y = 0

3x + 4y = 20

Now, take a graph paper and plot the following points:

A(0, 0)

B(2, 1)

P(0, 5)

Q(4, 2)

two lines intersect at the point Q (4, 2). Therefore, point Q lies on the lines represented by both the equations, x – 2y = 0 and 3x + 4y = 20. Hence, (4, 2) is the solution of this pair of equations in two variables. Let’s verify it algebraically:

x – 2y = 4 – 2(2) = 4 – 4 = 0 = RHS

3x + 4y = 3(4) + 4(2) = 12 + 8 = 20 = RHS