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Algebra 51378 Modules, Week 5 Assignment: Systems of Linear Equations and Problem Solving.

Twice the first number plus the second number is three. Find four × a number plus three × a second number. Provide your answer below.

a) 9, 3
b) 3, 9
c) -3, 3
d) 3, -3

1 Answer

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Final answer:

The correct answer is (d) 3, -3. The values 3 for the first number and -3 for the second number satisfy both conditions described: 2x + y = 3 and 4x + 3y, with the latter yielding a result of 3.

Step-by-step explanation:

To solve the question of finding two numbers based on given conditions, we can first define the variables: let x be the first number and y be the second number.

According to the first condition, we have an equation:2x + y = 3.

For the second condition in the question, we want to express 4x + 3y based on the given choices a) through d). To do this, when x and y meet the first condition, they will also satisfy the second since we are looking for a consistent solution that works for both conditions.

We can attempt to find the values of x and y by trying the pairs given in the answer choices and checking which one satisfies the first equation.

  • For choice (a) 9, 3: 2(9) + 3 = 18 + 3 = 21 ≠ 3. This does not satisfy the first equation.
  • For choice (b) 3, 9: 2(3) + 9 = 6 + 9 = 15 ≠ 3. This also does not satisfy the first equation.
  • For choice (c) -3, 3: 2(-3) + 3 = -6 + 3 = -3 ≠ 3. This does not satisfy the first equation either.
  • For choice (d) 3, -3: 2(3) + (-3) = 6 - 3 = 3. This satisfies the first equation.

Therefore, using the correct values from choice (d) to calculate 4x + 3y:

4(3) + 3(-3) = 12 - 9 = 3. The result is 3, which is based on the values of x and y from choice (d).