One number is seven less than five times another. if their sum is increased by one, the result is twelve. find the numbers

x = 8

y = 3

x = 5y - 7

x + y + 1 = 12

Because we have a value for x, we can use it in the second equation to find the value of y.

5y - 7 + y + 1 = 12

Combine like terms

6y - 6 = 12

Add 6 to both sides.

6y = 18

Divide both sides by 6.

y = 3

Now that we have a value for y we can place it back in the equation to find the value of x.

x + 3 + 1 = 12

Subtract 4 from both sides.

x = 8

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,