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−y−z=73x - y - z = 7\newline−2x+y+3z=−7-2x + y + 3z = -7\newline2x−2y+z=142x - 2y + z = 14

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−y−z=73x - y - z = 7\newline−2x+y+3z=−7-2x + y + 3z = -7\newline2x−2y+z=142x - 2y + z = 14
  1. Eliminate y by adding equations: First, let's add the first and second equations to eliminate y.\newline(3x−y−z)+(−2x+y+3z)=7+(−7)(3x - y - z) + (-2x + y + 3z) = 7 + (-7)\newline3x−y−z−2x+y+3z=03x - y - z - 2x + y + 3z = 0\newlinex+2z=0x + 2z = 0
  2. Simplify third equation: Now, let's multiply the third equation by 12\frac{1}{2} to simplify it.\newline(12)(2x−2y+z)=(12)(14)\left(\frac{1}{2}\right)(2x - 2y + z) = \left(\frac{1}{2}\right)(14)\newlinex−y+(12)z=7x - y + \left(\frac{1}{2}\right)z = 7
  3. Eliminate y by adding equations: Next, we'll add the modified third equation to the first equation to eliminate y. \newline(x−y+(1/2)z)+(3x−y−z)=7+7(x - y + (1/2)z) + (3x - y - z) = 7 + 7\newlinex−y+(1/2)z+3x−y−z=14x - y + (1/2)z + 3x - y - z = 14\newline4x−2y−(1/2)z=144x - 2y - (1/2)z = 14
  4. Eliminate z by adding equations: We can now add the new equation from the previous step to the modified second equation to eliminate z.\newline(4x−2y−12z)+(x+2z)=14+0(4x - 2y - \frac{1}{2}z) + (x + 2z) = 14 + 0\newline4x−2y−12z+x+2z=144x - 2y - \frac{1}{2}z + x + 2z = 14\newline5x−2y+32z=145x - 2y + \frac{3}{2}z = 14
  5. Get rid of fraction: Let's multiply the new equation by 22 to get rid of the fraction.\newline2(5x−2y+32z)=2(14)2(5x - 2y + \frac{3}{2}z) = 2(14)\newline10x−4y+3z=2810x - 4y + 3z = 28
  6. Eliminate y by adding equations: Now, we'll add the modified third equation to the new equation to eliminate y.\newline(10x−4y+3z)+(x−y+12z)=28+7(10x - 4y + 3z) + (x - y + \frac{1}{2}z) = 28 + 7\newline10x−4y+3z+x−y+12z=3510x - 4y + 3z + x - y + \frac{1}{2}z = 35\newline11x−5y+72z=3511x - 5y + \frac{7}{2}z = 35
  7. Solve for x: We can now solve for x by adding the first and third equations.\newline(3x−y−z)+(11x−5y+72z)=7+35(3x - y - z) + (11x - 5y + \frac{7}{2}z) = 7 + 35\newline3x−y−z+11x−5y+72z=423x - y - z + 11x - 5y + \frac{7}{2}z = 42\newline14x−6y+52z=4214x - 6y + \frac{5}{2}z = 42
  8. Divide to solve for x: Divide the new equation by 1414 to solve for xx.
    (14x−6y+(5/2)z)/14=42/14(14x - 6y + (5/2)z) / 14 = 42 / 14
    x−(6/14)y+(5/28)z=3x - (6/14)y + (5/28)z = 3
    x=3+(6/14)y−(5/28)zx = 3 + (6/14)y - (5/28)z

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