Question

a first number plus twice a second number is 9. twice the first number plus the second totals 21. find the numbers.
the smaller of the two numbers is
the larger of the two numbers is

Explanation:

Step1: Define variables

Let the first number be \( x \) and the second number be \( y \). From the problem, we have two equations:

1. \( x + 2y = 9 \)
2. \( 2x + y = 21 \)

Step2: Solve the system of equations

We can use the elimination method. First, multiply the first equation by 2: \( 2x + 4y = 18 \). Then subtract the second equation (\( 2x + y = 21 \)) from this new equation:

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Now substitute \( y = - 1 \) into the first equation \( x+2(-1)=9 \), so \( x - 2 = 9 \), then \( x=9 + 2=11 \).

Step3: Determine the smaller and larger number

We have \( x = 11 \) and \( y=-1 \). Since \( - 1<11 \), the smaller number is \( - 1 \) and the larger number is \( 11 \).

Answer:

The smaller of the two numbers is \(-1\). The larger of the two numbers is \(11\).