QQuestionMathematics
QuestionMathematics
Equation 1: x minus y, equals 1. Equation 2: x plus y equals, x squared minus 3
Which ordered pair is a solution to the system of equations above?
A. 1 plus the square root of 3, comma, the square root of 3
B. 1 plus the square root of 3, comma, the negative of the square root of 3
C. 1 plus the square root of 5, comma, the square root of 5
D. 1 plus the square root of 5, comma, negative 1 plus the square root of 5
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:: Identify the given system of equations.
Equation 2: $$x + y = x^2 - 3
Step 2:: To check which ordered pair is a solution to the system of equations, substitute the values of both x and y from each option into both equations and verify if they hold true.
(1 + \sqrt{3}) + \sqrt{3} = 1 + 2\sqrt{3} \neq (1 + \sqrt{3})^2 - 3$$ (since $$(1 + \sqrt{3})^2 - 3 = 4$$)
Checking Equation 1: Checking Equation 2: So, option A is not a solution.
Step 3:: Repeat the process for the other options.
2\sqrt{3} = 0
Checking Equation 1: Checking Equation 2: Since the last equation is not true, option B is not a solution.
Step 4:: Check the remaining options.
1 + 2\sqrt{5} = 1 + 2\sqrt{5}
Checking Equation 1: Checking Equation 2: Since both equations hold true, option C is a solution.
Step 5:: Check the last option for confirmation.
(1 + \sqrt{5}) - (-1 + \sqrt{5}) = 1 + \sqrt{5} + 1 - \sqrt{5} = 2
Checking Equation 1: Since the value does not match the right-hand side of Equation 1, option D is not a solution.
Final Answer
The ordered pair (1 + √5, √5) is a solution to the given system of equations.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students