Question

draw the graph of X+ Y= 4 and 3X+5Y=15 linear equations in two variables​

Answer 1

Step-by-step explanation:

Given :-

X+ Y= 4 and

3X+5Y=15

To find:-

Draw the graph of the given linear equations in two variables ?

Solution:-

Given pair of linear equations in two variables is

X+Y = 4

=> X+Y-4 = 0 ----------(1)

On Comparing this with a1x+b1y+c1 = 0 then

a1 = 1 , b1 = 1 , c1 = -4

3X+5Y = 15

=> 3X+5Y-15 = 0 ------(2)

On Comparing this with a2x+b2y+c2 = 0 then

a2 = 3 , b2 = 5 , c1 = -15

Now ,

a1/a2 = 1/3

b1/b2 = 1/5

c1/c2 = -4/-15 = 4/15

a1/a2 ≠ b1/b2 ≠ c1/c2

So, Given pair of linear equations in two variables are consistent and independent lines or intersecting lines with an unique solution.

Scale :-

On X-axis 1 cm = 1 unit

On Y-axis 1 cm = 1 unit

Observations:-

• The graph of the given equations are straight lines.
• They intersect at (5/2,0) and (0,3/2)
• The Solution = (5/2,3/2) = (2.5,1.5)

Answer:-

The graph of the given equations intersecting lines.

Used formulae:-

Let a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are the pair of linear equations in two variables then,

• If a1/a2 ≠b1/b2 ≠ c1/c2 then they are Consistent and Independent or intersecting lines with only one solution.
• If a1/a2 =b1/b2 ≠ c1/c2 then they are Inconsistent lines or Parallel lines lines with nosolution.
• If a1/a2 =b1/b2 = c1/c2 then they are Consistent and dependent or Coincident lines with many solutions.