Solve the system using elimination: 3x + 4y = 11 and -3x + 4y = 1. Which pair (x, y) satisfies both equations?

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

Master the Praxis Mathematics (5165) Test. Enhance your skills with flashcards and practice questions, each with detailed explanations. Ace your exam confidently!

Multiple Choice

Solve the system using elimination: 3x + 4y = 11 and -3x + 4y = 1. Which pair (x, y) satisfies both equations?

Explanation:
Elimination works well here because the x-terms have opposite coefficients, so adding the two equations cancels x and leaves an equation in y. Add the equations: (3x + 4y) + (-3x + 4y) = 11 + 1, which gives 8y = 12, so y = 12/8 = 3/2. With y found, plug into one equation to solve for x. Using 3x + 4y = 11 and y = 3/2: 3x + 4*(3/2) = 11, so 3x + 6 = 11, hence 3x = 5 and x = 5/3. Check in the other equation: -3x + 4y = 1 becomes -3*(5/3) + 4*(3/2) = -5 + 6 = 1, which matches. So the pair that satisfies both equations is x = 5/3 and y = 3/2.

Elimination works well here because the x-terms have opposite coefficients, so adding the two equations cancels x and leaves an equation in y.

Add the equations: (3x + 4y) + (-3x + 4y) = 11 + 1, which gives 8y = 12, so y = 12/8 = 3/2.

With y found, plug into one equation to solve for x. Using 3x + 4y = 11 and y = 3/2: 3x + 4*(3/2) = 11, so 3x + 6 = 11, hence 3x = 5 and x = 5/3.

Check in the other equation: -3x + 4y = 1 becomes -3*(5/3) + 4*(3/2) = -5 + 6 = 1, which matches.

So the pair that satisfies both equations is x = 5/3 and y = 3/2.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy