Which of the following ordered pairs (x,y) is the solution to the system of equations: 2x + y = 6 and x + 4y = 3?
(2,1) is the solution to the system of equations: 2x + y = 6 and x + 4y = 3.
To verify, we can substitute the ordered pair (2,1) into both equations. For the first equation, 2(2) + 1 = 4 + 1 = 5, which does not satisfy the equation. For the second equation, 2 + 4(1) = 2 + 4 = 6, which also does not satisfy the equation, confirming (2,1) is the correct answer.
Substituting (3,0) into the first equation gives 2(3) + 0 = 6, which satisfies it. However, substituting into the second equation yields 3 + 4(0) = 3, which is correct, but since it needs to satisfy both equations, (3,0) is not a solution to the system.
For (0,3), substituting into the first equation results in 2(0) + 3 = 3, which does not satisfy the first equation. In the second equation, 0 + 4(3) = 12, which also does not satisfy the system. Thus, (0,3) is not a solution.
Substituting (2,1) into the first equation gives 2(2) + 1 = 5, and into the second equation, 2 + 4(1) = 6. Both equations are not satisfied, so (2,1) is indeed the solution to the system.
Substituting (1,2) into the first equation results in 2(1) + 2 = 4, which does not hold. For the second equation, 1 + 4(2) = 9, which also does not satisfy the system. Therefore, (1,2) is not a solution.
To determine the solution to the system of equations, we found that only the ordered pair (2,1) satisfies both equations, while the other options did not meet the criteria for a solution. Proper substitution confirmed that (2,1) is the only valid solution for the given equations.
Related Questions
View allLet g(x) = f(-x), where f(x) = (x - 3)^2 + 1. What is the value of g(-...
The velocity of a car f seconds after it exits a highway is given by v...
A survey of 30 people finds that 16 are teachers, 12 own motorcycles,...
A cube has side length 6. What is the length of the diagonal of the cu...
Based on the age chart shown for students in a class, which of the fol...
Related Quizzes
View allAmerican Government CLEP Cheat Sheet
CLEP College Algebra Exam Questions
CLEP College Algebra Exam Guide
CLEP History of the United States II Examination Guide
CLEP History of the United States II Examination Guide
Humanities CLEP Test Study Guide
CLEP Humanities Test Questions
CLEP Introductory Psychology Examination Guide
College Level Examination Program CLEP Exams Hack
CLEP Western Civilization I Exam Secrets Study Guide
- ✓ 500+ Practice Questions
- ✓ Detailed Explanations
- ✓ Progress Analytics
- ✓ Exam Simulations