Solve the system: x + 2y = 7 and 3x - y = -1. The solution is

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 $9.99Unlock all

Study for the 8th Grade FAST Mathematics Pre-Algebra Test. Enhance your skills with interactive flashcards and multiple choice questions, each containing hints and explanations to boost your comprehension and readiness for the exam. Get ready to ace your test!

Multiple Choice

Solve the system: x + 2y = 7 and 3x - y = -1. The solution is

Explanation:
Solving a system of linear equations often uses substitution: solve one equation for one variable and plug that expression into the other. From the second equation, y = 3x + 1. Put that into the first equation: x + 2(3x + 1) = 7 x + 6x + 2 = 7 7x + 2 = 7 7x = 5 x = 5/7 Now find y: y = 3x + 1 = 3(5/7) + 1 = 15/7 + 7/7 = 22/7 Check quickly: x + 2y = 5/7 + 44/7 = 49/7 = 7 3x − y = 15/7 − 22/7 = −7/7 = −1 So the solution is x = 5/7 and y = 22/7.

Solving a system of linear equations often uses substitution: solve one equation for one variable and plug that expression into the other.

From the second equation, y = 3x + 1.

Put that into the first equation:

x + 2(3x + 1) = 7

x + 6x + 2 = 7

7x + 2 = 7

7x = 5

x = 5/7

Now find y:

y = 3x + 1 = 3(5/7) + 1 = 15/7 + 7/7 = 22/7

Check quickly:

x + 2y = 5/7 + 44/7 = 49/7 = 7

3x − y = 15/7 − 22/7 = −7/7 = −1

So the solution is x = 5/7 and y = 22/7.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy