Linear Equations in Two Variables Test - 7

only one because if a line is passing through two points then that two points are solution of a single linear equation

so only one line passes over two given points. 

becase one point can be solution of many equation

so many equation can be pass from one point

A linear equation in two variables is of the form ax + by + c = 0 as a and b are cofficient of x and y

 so if a = 0 and b = 0 or either of one is zero in that  case the equation will be one variable or their will be no equation respectively. 

therefore when a ≠ 0 and b ≠ 0 then only the equation will be in two variable

The equation of a line parallel to x-axis and 3 units above the origin is

y = 3

because when a line parallel to x axis in that case equation of line is y = a

where a is the co-ordinate of y-axis and 3 units above the origin value x -cordinate is 3

so required equation is y = 3

The equation of a line parallel to x-axis and 5 units below the origin is

y = -5

because when a line parallel to x axis in that case equation of line is y = a

where a is the co-ordinate of y-axes and 5 units below the origin value x -coordinate is -5

so required equation is y = -5

The equation of a line parallel to y-axis at a distance of 4 units from it, to its right  from the origin. 

x = 4

because when a line parallel to y axis in that case equation of line is x = 4

so required equation is x = 4

The equation of a line parallel to y-axis and 7 units to the left of the origin is

x = -7

because when a line parallel to y axis in that case equation of line is x = a

where a is the co-ordinate of x-axis and 7 units to the left of the origin value x -co-ordinate is -7

so required equation is x = -7

If the line represented by the equation 3x + ky = 9 passes through the points (2, 3) then (2,3) will satisy the equation 3x + ky = 9

3 (2) + 3k = 9
=>6 + 3k = 9
=>3k = 9-6
=>3k = 3
=> k = 1

y = 2x -7

Has many solution because for different value of x we have different value of y for example

At x = 1
y = 2 (1)-7
y = 2-7
y=-5

at x = 2
y = 2 (2)-7
y = 4-7
y=-3

So we can say for many value x there is many value of y

linear equation has solutions (-2, 2), (0, 0) and (2, -2), then the equation will be 

x + y = 0

As all the given three points satisfy the given equation