Respuesta :
Answer:
see the explanation
Step-by-step explanation:
Let
x ----> the smaller number
y ----> the larger number
we know that
A larger number is 2 more than 4 times a smaller number
Identify the key words
is (=)---> equal
more (+) ---> addition
times (*) ---> multiplication
That means
The larger number y is equal to multiply the smaller number x by 4 and then adds 2
so
[tex]y=4x+2[/tex] ----> equation A
The larger number is also 8 more than 2 times the smaller number
Identify the key words
is (=)---> equal
more (+) ---> addition
times (*) ---> multiplication
That means
The larger number y is equal to multiply the smaller number x by 2 and then adds 8
so
[tex]y=2x+8[/tex] ----> equation B
Solve the system of equations by substitution
equate equation A and equation B
[tex]4x+2=2x+8[/tex]
[tex]4x-2x=8-2\\2x=6\\x=3[/tex]
Find the value of y
substitute the value of x in equation A or equation B
[tex]y=4(3)+2=14[/tex]
therefore
The smaller number is 3 and the larger number is 14