The difference of two numbers is eight the first number x is one less than twice the second number y write and solve a system of linear equations to find the two numbers

The two numbers are 17 and 9.

System of Equations

Let x and y represent the first and second numbers, respectively.

... x - y = 8 . . . . . . . . . the difference of the two numbers is 8

... x = 2y - 1 . . . . . . . . .the first number is one less than twice the second

Solution

The second equation gives an expression for x that can be substituted into the first equation.

... (2y -1) -y = 8

... y -1 = 8 . . . . . . . collect terms

... y = 9 . . . . . . . . . add 1

... x = 2·9 -1 = 18 -1

... x = 17

The first number is 17; the second number is 9.

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