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:

How many solutions does the system of equations below have?\newline2x+2y−2z=−102x + 2y - 2z = -10\newline−x−2y−3z=15-x - 2y - 3z = 15\newline2x+3y+2z=−202x + 3y + 2z = -20\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions

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

Full solution

Q. How many solutions does the system of equations below have?\newline2x+2y−2z=−102x + 2y - 2z = -10\newline−x−2y−3z=15-x - 2y - 3z = 15\newline2x+3y+2z=−202x + 3y + 2z = -20\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Write Equations: First, let's write down the system of equations to see what we're working with:\newline11) 2x+2y−2z=−102x + 2y - 2z = -10\newline22) −x−2y−3z=15-x - 2y - 3z = 15\newline33) 2x+3y+2z=−202x + 3y + 2z = -20
  2. Eliminate Variable yy: We can try to simplify the system by adding equations (11) and (22) to eliminate the variable yy. So, (2x+2y−2z)+(−x−2y−3z)=−10+15(2x + 2y - 2z) + (-x - 2y - 3z) = -10 + 15 This simplifies to x−5z=5x - 5z = 5
  3. Correct Mistake: Now let's add equations (11) and (33) to eliminate yy again. So, (2x+2y−2z)+(2x+3y+2z)=−10−20(2x + 2y - 2z) + (2x + 3y + 2z) = -10 - 20 This simplifies to 4x+5y=−304x + 5y = -30 But wait, I made a mistake here. I should have canceled yy, not kept it. Let's correct that.

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 (29)