College algebra hw

Question

One number is six more than a second number. Four times the first is 3 less than 5 times the second. Find the numbers

Answer 1

One number x is six more than a second number y

x=6+y

Four times the first is 3 less than 5 times the second.

4x=5y-3

Now we substitute the x=6+y into the second equation

4(6+y)=5y-3

Distribute the 4

24+4y=5y-3

Subtract the 4y from both sides

24=y-3

Add 3 to both sides

y=27

Plug this y value into the first equation to obtain the x value

x=6+y

x=6+27=33

To check

33 is 6 more than 27

4 times x which is 4(33) =132 equals

5 times the second minus 3

5(27) -3= 135-3=132