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.\newline3x+3y−2z=−143x + 3y - 2z = -14\newlinex−y+2z=20x - y + 2z = 20\newline3x+y−3z=−153x + y - 3z = -15

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.\newline3x+3y−2z=−143x + 3y - 2z = -14\newlinex−y+2z=20x - y + 2z = 20\newline3x+y−3z=−153x + y - 3z = -15
  1. Combine Equations to Eliminate zz: First, let's eliminate zz from the first and third equations by adding them.\newline3x+3y−2z=−143x + 3y - 2z = -14\newline3x+y−3z=−153x + y - 3z = -15\newlineAdd the equations:\newline(3x+3y−2z)+(3x+y−3z)=−14+(−15)(3x + 3y - 2z) + (3x + y - 3z) = -14 + (-15)\newline6x+4y−5z=−296x + 4y - 5z = -29
  2. Multiply and Add Equations to Eliminate zz: Now, let's eliminate zz from the second and third equations by multiplying the second equation by 33 and adding it to the third equation.\newline3(x−y+2z)=3(20)3(x - y + 2z) = 3(20)\newline3x−3y+6z=603x - 3y + 6z = 60\newlineNow add this to the third equation:\newline(3x−3y+6z)+(3x+y−3z)=60+(−15)(3x - 3y + 6z) + (3x + y - 3z) = 60 + (-15)\newline6x−2y+3z=456x - 2y + 3z = 45
  3. Subtract Equations to Eliminate xx: We now have two new equations without zz:6x+4y−5z=−296x + 4y - 5z = -296x−2y+3z=456x - 2y + 3z = 45Let's eliminate xx by subtracting the second equation from the first.(6x+4y)−(6x−2y)=−29−45(6x + 4y) - (6x - 2y) = -29 - 456x+4y−6x+2y=−746x + 4y - 6x + 2y = -746y=−746y = -74y=−746y = \frac{-74}{6}y=−12.333y = -12.333

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 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 (41)