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+3y=2],[2x+6y=4]:} One Solution Infinitely Many Solutions No Solutions

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.\newlinex+3y=22x+6y=4 \begin{aligned} x+3 y & =2 \\ 2 x+6 y & =4 \end{aligned} \newlineOne Solution\newlineInfinitely Many Solutions\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+3y=22x+6y=4 \begin{aligned} x+3 y & =2 \\ 2 x+6 y & =4 \end{aligned} \newlineOne Solution\newlineInfinitely Many Solutions\newlineNo Solutions
  1. Given Equations: We are given the system of equations:\newlinex+3y=2x + 3y = 2\newline2x+6y=42x + 6y = 4\newlineFirst, we observe that the second equation is just the first equation multiplied by 22. This suggests that the two equations may actually be the same line, which would mean they have infinitely many solutions in common. However, we need to verify this by simplifying the equations further.
  2. Observation: Let's divide the second equation by 22 to see if it becomes identical to the first equation:\newline(2x+6y)/2=4/2(2x + 6y) / 2 = 4 / 2\newlinex+3y=2x + 3y = 2\newlineNow we can see that the second equation simplifies to the first equation, confirming that they are indeed the same line.
  3. Verification: Since both equations represent the same line, every point on that line is a solution to the system. Therefore, the system does not have a unique solution or no solution; instead, it has 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)