The sum of three integers is 189. the first integer is 28 less than the second. the second integer is 21 less than the sum of the first and third integer. find the three integers

The first integer is 56

The second integer is 84

The third integer is 49

Step-by-step explanation:

Define the variables

Let

x ----> the first integer

y ----> the second integer

z ----> the third integer

we know that

----> equation A

----> ----> equation B

----> equation C

Equate equations B and C

subtract x both sides

Adds 21 both sides

substitute the value of z in equation A

-----> equation D

Solve the system of equations B and D

----> equation B

-----> equation D

substitute equation B in equation D and solve for x

Find the value of y

----->

therefore

The first integer is 56

The second integer is 84

The third integer is 49

agree

step-by-step explanation:

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.