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 by substitution. {:[-x+6y=30],[-y-2=x]:} (◻,◻)

Solve the system by substitution.\newline−x+6y=30−y−2=x \begin{aligned} -x+6 y & =30 \\ -y-2 & =x \end{aligned} \newline(□,□) (\square, \square)

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 by substitution.\newline−x+6y=30−y−2=x \begin{aligned} -x+6 y & =30 \\ -y-2 & =x \end{aligned} \newline(□,□) (\square, \square)
  1. Solve for xx: Solve the second equation for xx. The second equation is −y−2=x-y - 2 = x. We can rewrite this as x=−y−2x = -y - 2.
  2. Substitute xx: Substitute xx in the first equation with the expression found in Step 11.\newlineThe first equation is −x+6y=30-x + 6y = 30. Substituting xx gives us −(−y−2)+6y=30-(-y - 2) + 6y = 30.
  3. Simplify the equation: Simplify the equation from Step 22.\newlineThis simplifies to y+2+6y=30y + 2 + 6y = 30, which further simplifies to 7y+2=307y + 2 = 30.
  4. Solve for y: Solve for y.\newlineSubtract 22 from both sides to get 7y=287y = 28. Then divide both sides by 77 to find y=4y = 4.
  5. Substitute yy: Substitute yy back into the equation x=−y−2x = -y - 2 to find xx. Substitute y=4y = 4 into x=−y−2x = -y - 2 to get x=−4−2x = -4 - 2, which simplifies to x=−6x = -6.
  6. Write the solution: Write the solution as an ordered pair x,yx, y. The solution is (−6,4)\left(-6, 4\right).

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)