Problem

A first number plus twice a second number is 7 . Twice the first number plus the second totals 32 . Find the numbers.

Answer

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Answer

The solution to the system of equations is \(\boxed{(19, -6)}\)

Steps

Step 1 ：Let's denote the first number as x and the second number as y.

Step 2 ：The problem can be represented as follows: \(x + 2y = 7\) and \(2x + y = 32\)

Step 3 ：Solve the first equation for x to get \(x = 7 - 2y\)

Step 4 ：Substitute \(x = 7 - 2y\) into the second equation to get \(14 - 3y = 32\)

Step 5 ：Solve for y to get \(y = -6\)

Step 6 ：Substitute \(y = -6\) into the first equation to get \(x = 19\)

Step 7 ：The solution to the system of equations is \(\boxed{(19, -6)}\)

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