For each part below, give an example of a linear system of
equations in two variables that has the given property. in each case, draw the lines
corresponding to the solutions of the equations in the system.
(a) has no solution
(b) has exactly one solution
(c) has infinitely many solutions
(i) add or remove equations in (b) to make an inconsistent system.
(ii) add or remove equations in (b) to create infinitely many solutions.
(iii) add or remove equations in (b) so that the solution space remains unchanged.
(iv) can you add or remove equations in (b) to change the unique solution you had
to a different unique solution?
in each of (i) - (iv) justify your action in words.

a)g: 3x + 4y = 10   b) a:x+y = 5           c) c: 3x + 4y = 10

h: 6x + 8y = 5         b:2x + 3y = 8         d: 6x + 8y = 5

Step-by-step explanation:

a) Has no solution

g: 3x + 4y = 10

h: 6x + 8y = 5

Above Equations  gives  you  parallel lines refer attachment

b) has exactly one solution

a:x+y = 5

b:2x + 3y = 8

Above Equations  gives  you  intersecting lines refer attachment

c) has infinitely many solutions

c: 3x + 4y = 10

d: 6x + 8y = 5

Above Equations  gives  you  collinear lines refer attachment

i) if we add   x + 2y = 1 to equation x + y = 5 to make an inconsistent system.

ii) if we add   x + 2y = 3 to equation x + y = 5 to create infinitely system.

iii) if we add  x + 4y = 1 to equation x + y = 5 to create infinitely system.

iv) if we add to x + y =5 equation x + y = 5  to change the unique solution you had  to a different unique solution

3

step-by-step explanation:

because where the point where the 2 lines intersect is (3,-1) the x value is 3

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.