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+26x−47y = x^2 + 26x - 47\newliney=26x+97y = 26x + 97\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\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=x2+26x−47y = x^2 + 26x - 47\newliney=26x+97y = 26x + 97\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: Set the two equations equal to each other since they both equal yy.y=x2+26x−47y = x^2 + 26x - 47y=26x+97y = 26x + 97So, x2+26x−47=26x+97x^2 + 26x - 47 = 26x + 97.
  2. Subtract to Zero: Subtract 26x+9726x + 97 from both sides to set the equation to zero.\newlinex2+26x−47−26x−97=0x^2 + 26x - 47 - 26x - 97 = 0\newlineThis simplifies to x2−144=0x^2 - 144 = 0.
  3. Factor Quadratic Equation: Factor the quadratic equation. x2−144=(x−12)(x+12)=0x^2 - 144 = (x - 12)(x + 12) = 0
  4. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−12=0x - 12 = 0 or x+12=0x + 12 = 0\newlineThis gives us x=12x = 12 or x=−12x = -12.
  5. Substitute x Values: Substitute x=12x = 12 into one of the original equations to find the corresponding yy value.\newlineUsing y=26x+97y = 26x + 97, we get y=26(12)+97=312+97=409y = 26(12) + 97 = 312 + 97 = 409.
  6. Write Coordinate Points: Substitute x=−12x = -12 into the same equation to find the corresponding yy value.\newlineUsing y=26x+97y = 26x + 97, we get y=26(−12)+97=−312+97=−215y = 26(-12) + 97 = -312 + 97 = -215.
  7. Write Coordinate Points: Substitute x=−12x = -12 into the same equation to find the corresponding yy value.\newlineUsing y=26x+97y = 26x + 97, we get y=26(−12)+97=−312+97=−215y = 26(-12) + 97 = -312 + 97 = -215.Write the solution as coordinate points.\newlineThe coordinate points are (12,409)(12, 409) and (−12,−215)(-12, -215).

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)