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. {:[-4x+4y=-40],[y=3x-4]:}

Solve the system by substitution.\newline−4x+4y=−40y=3x−4 \begin{aligned} -4 x+4 y & =-40 \\ y & =3 x-4 \end{aligned}

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−4x+4y=−40y=3x−4 \begin{aligned} -4 x+4 y & =-40 \\ y & =3 x-4 \end{aligned}
  1. Substitute yy with 3x−43x - 4: Substitute yy with 3x−43x - 4 in the first equation.\newlineThe first equation is −4x+4y=−40-4x + 4y = -40 and the second equation gives us y=3x−4y = 3x - 4. We will substitute yy in the first equation with the expression from the second equation.\newline−4x+4(3x−4)=−40-4x + 4(3x - 4) = -40
  2. Distribute and simplify: Distribute 44 into the parentheses and simplify.\newline−4x+12x−16=−40-4x + 12x - 16 = -40\newlineCombine like terms.\newline8x−16=−408x - 16 = -40
  3. Combine like terms: Add 1616 to both sides of the equation to isolate the term with xx.\newline8x−16+16=−40+168x - 16 + 16 = -40 + 16\newline8x=−248x = -24
  4. Add 1616 to isolate xx: Divide both sides by 88 to solve for xx.\newline8x8=−248\frac{8x}{8} = \frac{-24}{8}\newlinex=−3x = -3
  5. Divide by 88 for xx: Substitute x=−3x = -3 into the second equation to solve for yy. The second equation is y=3x−4y = 3x - 4. Substitute −3-3 for xx. y=3(−3)−4y = 3(-3) - 4
  6. Substitute xx into second equation: Multiply and subtract to find the value of yy.\newliney=−9−4y = -9 - 4\newliney=−13y = -13

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)