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. −8y+9x=−5-8y + 9x = -5 and 8y+7x=−758y + 7x = -75

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. −8y+9x=−5-8y + 9x = -5 and 8y+7x=−758y + 7x = -75
  1. Combine equations: Add the two equations to eliminate the variable yy.
    −8y+9x=−5-8y + 9x = -5
    8y+7x=−758y + 7x = -75
    (−8y+9x)+(8y+7x)=−5+(−75)(-8y + 9x) + (8y + 7x) = -5 + (-75)
  2. Eliminate variable yy: Perform the addition to eliminate yy.
    −8y+8y+9x+7x=−5−75-8y + 8y + 9x + 7x = -5 - 75
    0y+16x=−800y + 16x = -80
    16x=−8016x = -80
  3. Solve for x: Solve for x by dividing both sides of the equation by 1616.\newline16x16=−8016\frac{16x}{16} = \frac{-80}{16}\newlinex=−5x = -5
  4. Substitute xx into equation: Substitute x=−5x = -5 into one of the original equations to solve for yy. We'll use the first equation −8y+9x=−5-8y + 9x = -5.
    −8y+9(−5)=−5-8y + 9(-5) = -5
    −8y−45=−5-8y - 45 = -5
  5. Isolate term with y: Add 4545 to both sides of the equation to isolate the term with y.\newline−8y−45+45=−5+45-8y - 45 + 45 = -5 + 45\newline−8y=40-8y = 40
  6. Solve for y: Solve for y by dividing both sides of the equation by -8＂).\(\newline\$-8y / -8 = 40 / -8\)\(\newline\)\(y = -5\)

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 3 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 3 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 3 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 3 months ago

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

Posted 3 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 3 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 3 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 2 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 2 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 3 months ago

View all (99)