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.\newline−x+y−z=11-x + y - z = 11\newliney=−4y = -4\newlinex+2y−z=−5x + 2y - z = -5

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.\newline−x+y−z=11-x + y - z = 11\newliney=−4y = -4\newlinex+2y−z=−5x + 2y - z = -5
  1. Substitute y=−4y = -4: Substitute y=−4y = -4 into −x+y−z=11-x + y - z = 11.
    −x+(−4)−z=11-x + (-4) - z = 11
    −x−4−z=11-x - 4 - z = 11
  2. Rearrange for x: Rearrange the equation to solve for x.\newline−x=11+z+4-x = 11 + z + 4\newlinex=−11−z−4x = -11 - z - 4\newlinex=−15−zx = -15 - z
  3. Substitute yy and xx: Substitute y=−4y = -4 and x=−15−zx = -15 - z into x+2y−z=−5x + 2y - z = -5.\newline(−15−z)+2(−4)−z=−5(-15 - z) + 2(-4) - z = -5\newline−15−z−8−z=−5-15 - z - 8 - z = -5\newline−23−2z=−5-23 - 2z = -5
  4. Solve for z: Solve for z.\newline−2z=−5+23-2z = -5 + 23\newline−2z=18-2z = 18\newlinez=18−2z = \frac{18}{-2}\newlinez=−9z = -9
  5. Substitute zz into xx: Substitute z=−9z = -9 into x=−15−zx = -15 - z.\newlinex=−15−(−9)x = -15 - (-9)\newlinex=−15+9x = -15 + 9\newlinex=−6x = -6
  6. Final solution: We already have y=−4y = -4 from the given equation.

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)