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:

{:[2x+3y=-8],[3y^(2)-8y=2x+10]:} If (x_(1),y_(1)) and (x_(2),y_(2)) are distinct solutions to the system of equations shown, what is the product of the x_(1) and x_(2) ? ◻

2x+3y=−82x+3y=-8 \newline3y2−8y=2x+103y^{2}-8y=2x+10\newline If (x1,y1)(x_{1},y_{1}) and (x2,y2)(x_{2},y_{2}) are distinct solutions to the system of equations shown, what is the product of the x1x_{1} and x2x_{2}?

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Write a quadratic function from its x-intercepts and another pointright chevron icon

Full solution

Q. 2x+3y=−82x+3y=-8 \newline3y2−8y=2x+103y^{2}-8y=2x+10\newline If (x1,y1)(x_{1},y_{1}) and (x2,y2)(x_{2},y_{2}) are distinct solutions to the system of equations shown, what is the product of the x1x_{1} and x2x_{2}?
  1. Solve for x: Solve the first equation for x: 2x=−8−3y2x = -8 - 3y, so x=−8−3y2x = \frac{-8 - 3y}{2}.
  2. Substitute xx: Substitute xx in the second equation: 3y2−8y=2((−8−3y)/2)+103y^{2} - 8y = 2((-8 - 3y)/2) + 10.
  3. Simplify equation: Simplify the second equation: 3y2−8y=−8−3y+103y^{2} - 8y = -8 - 3y + 10.
  4. Combine like terms: Combine like terms: 3y2−5y+8=03y^{2} - 5y + 8 = 0.
  5. Factor quadratic equation: Factor the quadratic equation: (3y−8)(y+1)=0(3y - 8)(y + 1) = 0.
  6. Find roots for y: Find the roots for y: y=83y = \frac{8}{3} or y=−1y = -1.
  7. Substitute yy into x1x_{1}: Substitute y=83y = \frac{8}{3} into x=−8−3y2x = \frac{-8 - 3y}{2} to find x1x_{1}: x1=−8−3(83)2x_{1} = \frac{-8 - 3(\frac{8}{3})}{2}.
  8. Calculate x1x_{1}: Calculate x1x_{1}: x1=(−8−8)/2=−16/2=−8x_{1} = (-8 - 8)/2 = -16/2 = -8.
  9. Substitute yy into x2x_{2}: Substitute y=−1y = -1 into x=−8−3y2x = \frac{-8 - 3y}{2} to find x2x_{2}: x2=−8−3(−1)2x_{2} = \frac{-8 - 3(-1)}{2}.
  10. Calculate x2x_{2}: Calculate x2x_{2}: x2=−8+32=−52x_{2} = \frac{-8 + 3}{2} = -\frac{5}{2}.
  11. Find product of x1x_{1} and x2x_{2}: Find the product of x1x_{1} and x2x_{2}: (−8)×(−52)(-8) \times \left(-\frac{5}{2}\right).
  12. Calculate product: Calculate the product: x1×x2=402=20x_{1} \times x_{2} = \frac{40}{2} = 20.

More problems from Write a quadratic function from its x-intercepts and another point

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 10 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 10 months ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 7 months ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 7 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 7 months ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 7 months ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 7 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 7 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 7 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 7 months ago

View all (106)

Related topics

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