Solve the system of equations: x + y = 6 and 2x - y = 12.

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 PSAT/NMSQT Test with our comprehensive quizzes. Use interactive flashcards and multiple-choice questions, complete with hints and explanations, to get ready for exam day!

Multiple Choice

Solve the system of equations: x + y = 6 and 2x - y = 12.

Explanation:
When solving a two-variable linear system, you look for the point where the two lines intersect, which you can find by eliminating one variable. Add the equations to cancel y: (x + y) + (2x − y) = 6 + 12, giving 3x = 18, so x = 6. Then substitute x = 6 into the first equation: 6 + y = 6, which yields y = 0. The intersection point is (6, 0). Check: 6 + 0 = 6 and 2(6) − 0 = 12, both true, so this is the solution.

When solving a two-variable linear system, you look for the point where the two lines intersect, which you can find by eliminating one variable. Add the equations to cancel y: (x + y) + (2x − y) = 6 + 12, giving 3x = 18, so x = 6. Then substitute x = 6 into the first equation: 6 + y = 6, which yields y = 0. The intersection point is (6, 0). Check: 6 + 0 = 6 and 2(6) − 0 = 12, both true, so this is the solution.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy