Linear Equations in Two Variables Test - 8

The positive solutions of the equation ax + by + c = 0 always lie in the 1st quadrant

Because in 1st quadrant both x and y have positive value.

there are many linear equations in ‘x’ and ‘y’ can be satisfied by x = 1, y = 2

for example

x + y = 3              x - y =-1

2x + y =4

and so on there are infinte number of examples

The graph of y = 4x will pass through the origin (0,0)

y = 4x

at x = 0

y = 4.0

y = 0

so the graph y = 4x will pass from point (0,0)

For finding  value of ‘k’,  we put x = 2 and y = -1 iin a equation  x + 3y – k = 0
x+3 y-k=0
2+3(-1)=k
2-3=k
k=-1

solution of the equation 3x – 2y = 7

is (1,-2) as it satisfy the given equation

3x – 2y = 7

=> 3(1) - 2(-2) = 7

=> 3+4=7

LHS = RHS

In linear equation power of variable x and y should be 1 and here,  the given linear equation has two variable x and y.