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:

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. {:[x+4y=-5],[4x+16 y=-20]:} Infinitely Many Solutions One Solution No Solutions

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.\newlinex+4y=−54x+16y=−20 \begin{aligned} x+4 y & =-5 \\ 4 x+16 y & =-20 \end{aligned} \newlineInfinitely Many Solutions\newlineOne Solution\newlineNo Solutions

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Determine the number of solutions to a system of equations in three variablesright chevron icon

Full solution

Q. Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.\newlinex+4y=−54x+16y=−20 \begin{aligned} x+4 y & =-5 \\ 4 x+16 y & =-20 \end{aligned} \newlineInfinitely Many Solutions\newlineOne Solution\newlineNo Solutions
  1. Given Equations: We are given the system of equations:\newline11. x+4y=−5x + 4y = -5\newline22. 4x+16y=−204x + 16y = -20\newlineLet's first simplify the second equation by dividing all terms by 44 to see if it gives us a clue about the relationship between the two equations.\newline4x4+16y4=−204\frac{4x}{4} + \frac{16y}{4} = \frac{-20}{4}\newlinex+4y=−5x + 4y = -5
  2. Simplify Second Equation: Now we have the simplified system:\newline11. x+4y=−5x + 4y = -5\newline22. x+4y=−5x + 4y = -5\newlineWe can see that both equations are identical, which means that every solution to the first equation is also a solution to the second equation.
  3. Identical Equations: Since both equations represent the same line, there are infinitely many points (x,y)(x, y) that satisfy both equations. Therefore, the system does not have a unique solution, but rather infinitely many solutions.

More problems from Determine the number of solutions to a system of equations in three variables

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 (23)