Solve the linear system 3x + y = 10 and x - 2y = 1.

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $24.99Unlock all

Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

Solve the linear system 3x + y = 10 and x - 2y = 1.

Explanation:
When solving a system of linear equations, you’re looking for the point where both equations hold true at the same time—the intersection of the two lines. From 3x + y = 10, express y as y = 10 − 3x. Substitute this into the second equation x − 2y = 1: x − 2(10 − 3x) = 1 ⇒ x − 20 + 6x = 1 ⇒ 7x = 21 ⇒ x = 3. Then y = 10 − 3x = 10 − 9 = 1. Check: 3x + y = 9 + 1 = 10 and x − 2y = 3 − 2 = 1, so both are satisfied. Thus the solution is x = 3, y = 1. Other given pairs don’t satisfy both equations (for example, x = 4, y = 0 gives 3x + y = 12, not 10), so they aren’t valid.

When solving a system of linear equations, you’re looking for the point where both equations hold true at the same time—the intersection of the two lines.

From 3x + y = 10, express y as y = 10 − 3x. Substitute this into the second equation x − 2y = 1: x − 2(10 − 3x) = 1 ⇒ x − 20 + 6x = 1 ⇒ 7x = 21 ⇒ x = 3. Then y = 10 − 3x = 10 − 9 = 1. Check: 3x + y = 9 + 1 = 10 and x − 2y = 3 − 2 = 1, so both are satisfied.

Thus the solution is x = 3, y = 1. Other given pairs don’t satisfy both equations (for example, x = 4, y = 0 gives 3x + y = 12, not 10), so they aren’t valid.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy