A number is made up of two digits. the sum of digits is 11, if the digits are interchanged, the original number is increased by 9. find the number

56

Step-by-step explanation:

let the 2 digits be a and b

Create 2 equations, solve simultaneously for a and b

a + b = 11 → ( 1) ( sum of digits )

The original number is ab, that is 10a + b ( considering place value )

Interchanging the 2 digits gives ba, that is 10b + a, thus

10b + a = 10a + b + 9 ( original number increased by 9 )

Subtract b from both sides

9b + a = 10a + 9 ( subtract 10a from both sides )

9b - 9a = 9 → (2)

Rearranging (1) expressing a in terms of b

a = 11 - b

Substitute a = 11 - b into (2)

9b - 9(11 - b) = 9 ← distribute and simplify left side

9b - 99 + 9b = 9

18b - 99 = 9 ( add 99 to both sides )

18b = 108 ( divide both sides by 18 )

b = 6

Substitute b = 6 into (1)

a + 6 = 11 ⇒ a = 5

The original number is 56

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

you already gave the answer

step-by-step explanation: