Questions: What are the ordered pair solutions for this system of equations? y=x^2-2x+3 y=-2x+12 First, set the equations equal to each other and move everything to one side. A: x^2+9=0 B: x^2-4x+15=0 C: x^2-9=0 D: x^2+15=0

What are the ordered pair solutions for this system of equations? y=x^2-2x+3 y=-2x+12 First, set the equations equal to each other and move everything to one side. A: x^2+9=0 B: x^2-4x+15=0 C: x^2-9=0 D: x^2+15=0

Solution

failed
failed

Solution Steps

To find the ordered pair solutions for the given system of equations, we need to set the two equations equal to each other and solve for \( x \). Once we have the values of \( x \), we can substitute them back into either equation to find the corresponding \( y \) values. This will give us the ordered pairs that satisfy both equations.

Step 1: Set the Equations Equal to Each Other

To find the points of intersection, set the two equations equal to each other: \[ x^2 - 2x + 3 = -2x + 12 \]

Step 2: Simplify and Solve for \( x \)

Rearrange the equation to bring all terms to one side: \[ x^2 - 2x + 3 + 2x - 12 = 0 \implies x^2 - 9 = 0 \] Solve for \( x \) by factoring: \[ (x - 3)(x + 3) = 0 \] Thus, the solutions for \( x \) are: \[ x = 3 \quad \text{and} \quad x = -3 \]

Step 3: Substitute \( x \) Values to Find Corresponding \( y \) Values

Substitute \( x = 3 \) into the second equation \( y = -2x + 12 \): \[ y = -2(3) + 12 = 6 \] Substitute \( x = -3 \) into the second equation \( y = -2x + 12 \): \[ y = -2(-3) + 12 = 18 \]

Final Answer

The ordered pair solutions for the system of equations are: \[ \boxed{(3, 6)} \quad \text{and} \quad \boxed{(-3, 18)} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Which of the following will pass through a cell membrane most easily? Multiple Choice Small polar molecules Small nonpolar molecules Large polar molecules Large nonpolar molecules Large neutral molecules
failedAnswered
Sales price: 5,600, 3,600 Variable cost of goods sold: (3,530), (2,410) Manufacturing margin: 2,070, 1,190 Variable selling expenses: (782), (650) Contribution margin: 1,288, 540 Fixed expenses: (610), (220) Operating income: 678, 320 Conquistador, Hurricane Sales unit volume: 2,200, 1,700 Prepare a contribution margin by product report. Compute the contribution margin ratio for each product as a whole percent for Galaxy Sports Inc.
failedAnswered
Skin-to-skin contact with their parents as an infant may improve Emerson's cognitive development for: the rest of their life. at least the first 10 years of their life. the first two or three years of life. just the first few months of life.
failedAnswered
Let U=k, l, m, n, o, p, q and A=k, o, p, q. Find A̅. A̅= (Use ascending order. Use a comma to separate answers as needed.)
failedAnswered
A waiver of the requirement for documentation of informed consent may be granted when: - The only record linking the subject and the research is the consent document and the principal risk is a breach of confidentiality. - The investigator has no convenient place to store signed consent forms separate from the research data. - Potential subjects might find some of the research questions embarrassing, personal, or intrusive. - The subjects are literate in their own language; however, they do not read, write, or speak English.