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 by elimination.\newline−x−3y+3z=−11-x - 3y + 3z = -11\newlinex+2y+z=2x + 2y + z = 2\newline3x−2y+2z=03x - 2y + 2z = 0

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve a system of equations in three variables using eliminationright chevron icon

Full solution

Q. Solve the system of equations by elimination.\newline−x−3y+3z=−11-x - 3y + 3z = -11\newlinex+2y+z=2x + 2y + z = 2\newline3x−2y+2z=03x - 2y + 2z = 0
  1. Eliminate xx by adding equations: Add the first and second equations to eliminate xx.
    (−x−3y+3z)+(x+2y+z)=−11+2(-x - 3y + 3z) + (x + 2y + z) = -11 + 2
    −x+x−3y+2y+3z+z=−9-x + x - 3y + 2y + 3z + z = -9
    −y+4z=−9-y + 4z = -9
  2. Prepare to eliminate xx: Multiply the second equation by 33 to prepare to eliminate xx with the third equation.\newline3(x+2y+z)=3(2)3(x + 2y + z) = 3(2)\newline3x+6y+3z=63x + 6y + 3z = 6
  3. Correct previous mistake: Add the new equation from Step 33 to the third equation to eliminate xx.(3x+6y+3z)+(3x−2y+2z)=6+0(3x + 6y + 3z) + (3x - 2y + 2z) = 6 + 03x+3x+6y−2y+3z+2z=63x + 3x + 6y - 2y + 3z + 2z = 66x+4y+5z=66x + 4y + 5z = 6
  4. Correct previous mistake: Add the new equation from Step 33 to the third equation to eliminate xx.\newline(3x+6y+3z)+(3x−2y+2z)=6+0(3x + 6y + 3z) + (3x - 2y + 2z) = 6 + 0\newline3x+3x+6y−2y+3z+2z=63x + 3x + 6y - 2y + 3z + 2z = 6\newline6x+4y+5z=66x + 4y + 5z = 6Oops, I made a mistake in the previous step. I should have subtracted the equations, not added them. Let's correct that.\newline(3x+6y+3z)−(3x−2y+2z)=6−0(3x + 6y + 3z) - (3x - 2y + 2z) = 6 - 0\newline3x−3x+6y+2y+3z−2z=63x - 3x + 6y + 2y + 3z - 2z = 6\newline8y+z=68y + z = 6

More problems from Solve a system of equations in three variables using elimination

Question
Solve using substitution. 5x−2y=−7 5x - 2y = -7 x=−5 x = -5 (_,_)
Get tutor helpright-arrow

Posted 6 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 6 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 6 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 6 months ago

Question
Solve. \newlinex=−2 x = -2 \newline−2x+2y=−8 -2x + 2y = -8 \newline(____,____)(\_\_\_\_, \_\_\_\_)
Get tutor helpright-arrow

Posted 10 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 10 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 6 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 6 months 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 6 months 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 6 months ago

View all (39)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant