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=10x−80y = 10x - 80\newliney=x2−12x+41y = x^2 - 12x + 41\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve a nonlinear system of equationsright chevron icon

Full solution

Q. Solve the system of equations.\newliney=10x−80y = 10x - 80\newliney=x2−12x+41y = x^2 - 12x + 41\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)
  1. Substitute y Equation: Substitute yy from the first equation into the second equation. Since y=10x−80y = 10x - 80, we can replace yy in the second equation y=x2−12x+41y = x^2 - 12x + 41 with 10x−8010x - 80. This gives us the equation 10x−80=x2−12x+4110x - 80 = x^2 - 12x + 41.
  2. Rearrange and Solve for x: Rearrange the equation to set it to zero and solve for x. This means we will subtract 10x10x and add 8080 to both sides of the equation.\newlineThe new equation is 0=x2−12x+10x+41−800 = x^2 - 12x + 10x + 41 - 80, which simplifies to 0=x2−2x−390 = x^2 - 2x - 39.
  3. Factor Quadratic Equation: Factor the quadratic equation x2−2x−39x^2 - 2x - 39. We are looking for two numbers that multiply to −39-39 and add up to −2-2. The numbers that satisfy these conditions are −9-9 and +7+7, so we can factor the equation as (x−9)(x+7)=0(x - 9)(x + 7) = 0.
  4. Solve for x: Solve for x by setting each factor equal to zero. This gives us two possible solutions for x: x−9=0x - 9 = 0 or x+7=0x + 7 = 0. Solving these, we get x=9x = 9 or x=−7x = -7.
  5. Substitute xx for yy: Substitute xx back into the original equation y=10x−80y = 10x - 80 to find the corresponding yy values.\newlineFirst, for x=9x = 9, we get y=10(9)−80y = 10(9) - 80, which simplifies to y=90−80y = 90 - 80, so y=10y = 10.
  6. Find y Values: Now, for x=−7x = -7, we substitute into y=10x−80y = 10x - 80 to get y=10(−7)−80y = 10(-7) - 80, which simplifies to y=−70−80y = -70 - 80, so y=−150y = -150.
  7. Final Solutions: We now have two solutions for the system of equations: (9,10)(9, 10) and (−7,−150)(-7, -150). These are the coordinates of the points where the two equations intersect.

More problems from Solve a nonlinear system of equations

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 (75)