Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If (x,y) is a solution to the system of equations shown, what is the product of the y-coordinates of the solutions? x^(2)+y^(2)=9 x+y=3

If (x,y) (x, y) is a solution to the system of equations shown, what is the product of the y y -coordinates of the solutions?\newlinex2+y2=9 x^{2}+y^{2}=9 \newlinex+y=3 x+y=3

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Evaluate recursive formulas for sequencesright chevron icon

Full solution

Q. If (x,y) (x, y) is a solution to the system of equations shown, what is the product of the y y -coordinates of the solutions?\newlinex2+y2=9 x^{2}+y^{2}=9 \newlinex+y=3 x+y=3
  1. Given Equations: We are given the system of equations:\newline11. x2+y2=9 x^2 + y^2 = 9 \newline22. x+y=3 x + y = 3 \newlineWe need to find the y-coordinates of the solutions to these equations and then calculate their product. Let's start by expressing x in terms of y using the second equation.\newlinex=3−y x = 3 - y
  2. Expressing x in terms of y: Now, we substitute x=3−y x = 3 - y into the first equation to find y.\newline(3−y)2+y2=9 (3 - y)^2 + y^2 = 9 \newlineExpanding the squared term, we get:\newline9−6y+y2+y2=9 9 - 6y + y^2 + y^2 = 9 \newlineSimplifying, we combine like terms:\newline2y2−6y=0 2y^2 - 6y = 0
  3. Substituting x into the first equation: We can factor out a y from the equation:\newliney(2y−6)=0 y(2y - 6) = 0 \newlineThis gives us two possible solutions for y:\newline11. y=0 y = 0 \newline22. 2y−6=0 2y - 6 = 0 which simplifies to y=3 y = 3
  4. Factoring out y: We have two y-coordinates for the solutions: y=0 y = 0 and y=3 y = 3 . To find the product of the y-coordinates, we multiply these two values together:\newlineProduct of y-coordinates = y1×y2=0×3=0 y_1 \times y_2 = 0 \times 3 = 0
  5. Finding the y-coordinates: The product of the y-coordinates of the solutions to the system of equations is 00.

More problems from Evaluate recursive formulas for sequences

Question
Find the sum of the finite arithmetic series. ∑n=110(7n+4)\sum_{n=1}^{10} (7n+4)\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`
Get tutor helpright-arrow

Posted 5 months ago

Question
Type the missing number in this sequence: `2, 4 8`, ______,`32`
Get tutor helpright-arrow

Posted 5 months ago

Question
What kind of sequence is this? 2,10,50,250,…2, 10, 50, 250, \ldots Choices:Choices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 5 months ago

Question
What is the missing number in this pattern? 1,4,9,16,25,36,49,64,81,____1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_
Get tutor helpright-arrow

Posted 7 months ago

Question
Classify the series. ∑n=012(n+2)3 \sum_{n = 0}^{12} (n + 2)^3 \newlineChoices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the first three partial sums of the series.\newline1+6+11+16+21+26+⋯1 + 6 + 11 + 16 + 21 + 26 + \cdots\newlineWrite your answers as integers or fractions in simplest form.\newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 7 months ago

Question
Find the third partial sum of the series. \newline3+9+15+21+27+33+⋯3 + 9 + 15 + 21 + 27 + 33 + \cdots\newlineWrite your answer as an integer or a fraction in simplest form. \newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 7 months ago

Question
Find the first three partial sums of the series. \newline1+7+13+19+25+31+⋯1 + 7 + 13 + 19 + 25 + 31 + \cdots\newlineWrite your answers as integers or fractions in simplest form. \newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 9 months ago

Question
Does the infinite geometric series converge or diverge?\newline1+34+916+2764+⋯1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots\newlineChoices:\newline[A]converge\text{[A]converge}\newline[B]diverge\text{[B]diverge}
Get tutor helpright-arrow

Posted 5 months ago

View all (18)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant