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. {:[-7y-5=x],[-3x+2y=-8]:} (◻,◻)

Solve the system by substitution.\newline−7y−5=x−3x+2y=−8 \begin{array}{c} -7 y-5=x \\ -3 x+2 y=-8 \end{array} \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−7y−5=x−3x+2y=−8 \begin{array}{c} -7 y-5=x \\ -3 x+2 y=-8 \end{array} \newline(□,□) (\square, \square)
  1. Isolate xx: Isolate xx in the first equation −7y−5=x-7y - 5 = x. Add 55 to both sides of the equation. −7y−5+5=x+5-7y - 5 + 5 = x + 5 −7y=x+5-7y = x + 5 Now, subtract 55 from both sides to get xx by itself. −7y−5=x-7y - 5 = x
  2. Substitute xx: Substitute −7y−5-7y - 5 for xx in the second equation −3x+2y=−8-3x + 2y = -8. Replace xx with −7y−5-7y - 5 in the second equation. −3(−7y−5)+2y=−8-3(-7y - 5) + 2y = -8
  3. Distribute and combine terms: Distribute −3-3 across the parentheses.\newline−3×−7y+(−3)×−5+2y=−8-3 \times -7y + (-3) \times -5 + 2y = -8\newline21y+15+2y=−821y + 15 + 2y = -8
  4. Isolate y-term: Combine like terms on the left side of the equation.\newline21y+2y+15=−821y + 2y + 15 = -8\newline23y+15=−823y + 15 = -8
  5. Solve for y: Subtract 1515 from both sides to isolate the y-term.\newline23y+15−15=−8−1523y + 15 - 15 = -8 - 15\newline23y=−2323y = -23
  6. Substitute yy into first equation: Divide both sides by 2323 to solve for yy.\newline23y23=−2323\frac{23y}{23} = \frac{-23}{23}\newliney=−1y = -1
  7. Find xx: Substitute y=−1y = -1 back into the first equation −7y−5=x-7y - 5 = x to solve for xx.
    −7(−1)−5=x-7(-1) - 5 = x
    7−5=x7 - 5 = x
    x=2x = 2
  8. Write solution: Write the solution as an ordered pair (x,y)(x, y).\newlineThe solution is (2,−1)(2, -1).

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)