One number is 13 less than another. Twice the larger is equal to 7 times the smaller increased by 1. find the numbers.

Answer: [tex]Larger\ number:\ 18[/tex] [tex]Smaller\ number:\ 5[/tex]Step-by-step explanation: Let be "x" the smaller number and "y" the larger number. According to information provided in the exercise, the smaller number is 13 less than the larger number. This can be expressed as: [tex]x=y-13[/tex] Twice the larger number (the larger number must be multiplied by 2) is equal to 7 times the smaller (the smaller number must be multiplied by 7) increased by 1 (this indicates that you need to add 1). Then, this is: [tex]2y=7x+1[/tex] Substitute the first equation into the second equation and solve for "y": [tex]2y=7(y-13)+1\\\\2y=7y-91+1\\\\90=5y\\\\y=18[/tex] Substitute this value into the first equation to find the value of "x": [tex]x=18-13\\\\x=5[/tex]