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:

{:[5x+3y=9],[2x-3y=12]:}

5x+3y=92x−3y=12 \begin{array}{l}5 x+3 y=9 \\ 2 x-3 y=12\end{array}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Solve a system of equations using any methodright chevron icon

Full solution

Q. 5x+3y=92x−3y=12 \begin{array}{l}5 x+3 y=9 \\ 2 x-3 y=12\end{array}
  1. Set up equations: Set up the system of equations given by the problem.\newlineWe have two equations:\newline11) 5x+3y=95x + 3y = 9\newline22) 2x−3y=122x - 3y = 12
  2. Add and eliminate yy: Add the two equations together to eliminate yy.
    (5x+3y)+(2x−3y)=9+12(5x + 3y) + (2x - 3y) = 9 + 12
    This simplifies to:
    5x+2x=215x + 2x = 21
  3. Combine like terms: Combine like terms to solve for xx.5x+2x=7x5x + 2x = 7x7x=217x = 21
  4. Solve for x: Divide both sides by 77 to find the value of x.\newline7x7=217\frac{7x}{7} = \frac{21}{7}\newlinex=3x = 3
  5. Substitute xx and solve: Substitute x=3x = 3 into one of the original equations to solve for yy. We'll use the first equation:\newline5x+3y=95x + 3y = 9\newline5(3)+3y=95(3) + 3y = 9
  6. Simplify and find yy: Simplify the equation and solve for yy.15+3y=915 + 3y = 93y=9−153y = 9 - 153y=−63y = -6
  7. Divide and find y: Divide both sides by 33 to find the value of y.\newline3y3=−63\frac{3y}{3} = \frac{-6}{3}\newliney=−2y = -2

More problems from Solve a system of equations using any method

Question
Solve using substitution. 5x−2y=−7 5x - 2y = -7 x=−5 x = -5 (_,_)
Get tutor helpright-arrow

Posted 5 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 5 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 5 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 5 months ago

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

Posted 8 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 8 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 5 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 5 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 5 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 5 months ago

View all (67)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant