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:

Solve the system of equations.\newliney=x2−36x−29y = x^2 - 36x - 29\newliney=−21x−43y = -21x - 43\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)\newline

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve a system of linear and quadratic equations: parabolasright chevron icon

Full solution

Q. Solve the system of equations.\newliney=x2−36x−29y = x^2 - 36x - 29\newliney=−21x−43y = -21x - 43\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)\newline
  1. Set Equations Equal: We have the following system of equations:\newliney=x2−36x−29y = x^2 - 36x - 29\newliney=−21x−43y = -21x - 43\newlineTo find the solution, we will set the two equations equal to each other since they both equal yy.\newlinex2−36x−29=−21x−43x^2 - 36x - 29 = -21x - 43
  2. Rearrange and Form Quadratic Equation: Rearrange the equation to bring all terms to one side and set it equal to zero to form a standard quadratic equation.\newlinex2−36x−29+21x+43=0x^2 - 36x - 29 + 21x + 43 = 0\newlinex2−15x+14=0x^2 - 15x + 14 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation.\newlineWe are looking for two numbers that multiply to 1414 and add up to −15-15. These numbers are −1-1 and −14-14.\newlinex2−15x+14=(x−1)(x−14)x^2 - 15x + 14 = (x - 1)(x - 14)
  4. Solve for x: Solve for x by setting each factor equal to zero.\newline(x−1)=0(x - 1) = 0 or (x−14)=0(x - 14) = 0\newlineThis gives us two solutions for x:\newlinex=1x = 1 and x=14x = 14
  5. Find Corresponding y-values: Find the corresponding y-values for each x-value by substituting back into either of the original equations. We'll use y=−21x−43y = -21x - 43.\newlineFor x=1x = 1:\newliney=−21(1)−43y = -21(1) - 43\newliney=−21−43y = -21 - 43\newliney=−64y = -64\newlineFor x=14x = 14:\newliney=−21(14)−43y = -21(14) - 43\newliney=−294−43y = -294 - 43\newliney=−337y = -337
  6. Write Coordinates: Write the coordinates in exact form.\newlineThe solutions to the system of equations are the points where the two graphs intersect, which are the xx-values we found and their corresponding yy-values.\newlineFirst Coordinate: (1,−64)(1, -64)\newlineSecond Coordinate: (14,−337)(14, -337)

More problems from Solve a system of linear and quadratic equations: parabolas

Question
Solve using substitution. 5x−2y=−7 5x - 2y = -7 x=−5 x = -5 (_,_)
Get tutor helpright-arrow

Posted 2 months ago

Question
Is (1,1)(1,1) a solution to this system of equations? \newline4x+10y=144x + 10y = 14\newlinex+6y=7x + 6y = 7\newlineChoices:\newline(A) yes \newline(B) no
Get tutor helpright-arrow

Posted 2 months ago

Question
Which describes the system of equations below?\newliney=–3x+9y = –3x + 9 \newliney=–3x+9y = –3x + 9 \newlineChoices:\newline(A) consistent and independent\text{(A) consistent and independent} \newline(B) consistent and dependent\text{(B) consistent and dependent} \newline(C) inconsistent\text{(C) inconsistent}
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve using elimination. \newline7x−8y=−17 7x - 8y = -17 \newline −7x+3y=2 -7x + 3y = 2 \newline (____,____)(\_\_\_\_, \_\_\_\_)
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve. \newlinex=−2 x = -2 \newline−2x+2y=−8 -2x + 2y = -8 \newline(____,____)(\_\_\_\_, \_\_\_\_)
Get tutor helpright-arrow

Posted 2 months ago

Question
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineAt a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases 33 hot dog meals and 33 hamburger meals, paying a total of $36\$36. Mr. Hogan buys 11 hot dog meal and 33 hamburger meals, spending $26\$26 in all. How much do the meals cost?\newlineHot dog meals cost $\$_______ each, and hamburger meals cost $\$________ each.
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations by substitution.\newline−3x−y−3z=−11-3x - y - 3z = -11\newlinez=5z = 5\newlinex−y+3z=19x - y + 3z = 19\newline(____.____,____)
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations by elimination.\newlinex−3y−2z=10 x - 3y - 2z = 10 \newline3x+2y+2z=14 3x + 2y + 2z = 14 \newline2x−3y−2z=16 2x - 3y - 2z = 16 \newline(_,_,_)(\_,\_,\_)
Get tutor helpright-arrow

Posted 1 month ago

Question
Solve the system of equations.\newliney=x2+36x+3 y = x^2 + 36x + 3 \newliney=22x−37 y = 22x - 37 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_)(\_,\_)\newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 1 month ago

Question
Solve the system of equations.\newliney=−x−24 y = -x - 24 \newlinex2+y2=488 x^2 + y^2 = 488 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_) (\_,\_) \newline(_,_) (\_,\_)
Get tutor helpright-arrow

Posted 2 months ago

View all (71)