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 substitution.\newline3x−2y+2z=−143x - 2y + 2z = -14\newlinex−y−3z=−16x - y - 3z = -16\newlinex=−6x = -6

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 substitutionright chevron icon

Full solution

Q. Solve the system of equations by substitution.\newline3x−2y+2z=−143x - 2y + 2z = -14\newlinex−y−3z=−16x - y - 3z = -16\newlinex=−6x = -6
  1. Substitute x=−6x = -6: Substitute x=−6x = -6 into the second equation, x−y−3z=−16x - y - 3z = -16.\newline−6−y−3z=−16-6 - y - 3z = -16.\newlineNow, solve for y.\newline−y−3z=−16+6-y - 3z = -16 + 6.\newline−y−3z=−10-y - 3z = -10.\newliney+3z=10y + 3z = 10.
  2. Substitute x=−6x = -6: Substitute x=−6x = -6 into the first equation, 3x−2y+2z=−143x - 2y + 2z = -14.
    3(−6)−2y+2z=−143(-6) - 2y + 2z = -14.
    −18−2y+2z=−14-18 - 2y + 2z = -14.
    Now, solve for yy.
    −2y+2z=−14+18-2y + 2z = -14 + 18.
    −2y+2z=4-2y + 2z = 4.
    Divide by −2-2.
    y−z=−2y - z = -2.
    x=−6x = -600.
  3. Solve for z: We have two expressions for y: y+3z=10y + 3z = 10 and y=z−2y = z - 2. Set them equal to each other to solve for z. z−2+3z=10z - 2 + 3z = 10. Combine like terms. 4z−2=104z - 2 = 10. Add 22 to both sides. 4z=124z = 12. Divide by 44. z=3z = 3.
  4. Find yy: Substitute z=3z = 3 into y=z−2y = z - 2 to find yy.\newliney=3−2y = 3 - 2.\newliney=1y = 1.
  5. Final Solution: We already have x=−6x = -6 and z=3z = 3, and we just found y=1y = 1. The solution is (−6,1,3)(-6, 1, 3).

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

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 (99)