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:

Lindsay is 5 years younger than Mark. Seven years ago, the sum of their ages was 31. Let l be Lindsay's age and let m be Mark's age. Which system of equations represents this situation? Choose 1 answer: (A) {[l=m+5],[(l-7)+(m-7)=3]:} (B) {[l-7=(m-7)-5],[l+m=31]:} (C) {[l=m-5],[(l-7)+(m-7)=3]:} (D) {[l-7=(m-7)+5],[l+m=31]:}

Lindsay is 55 years younger than Mark. Seven years ago, the sum of their ages was 3131 .\newlineLet l l be Lindsay's age and let m m be Mark's age.\newlineWhich system of equations represents this situation?\newlineChoose 11 answer:\newline(A) {l=m+5(l−7)+(m−7)=3 \left\{\begin{array}{l}l=m+5 \\ (l-7)+(m-7)=3\end{array}\right. \newline(B) {l−7=(m−7)−5l+m=31 \left\{\begin{array}{l}l-7=(m-7)-5 \\ l+m=31\end{array}\right. \newline(C) {l=m−5(l−7)+(m−7)=3 \left\{\begin{array}{l}l=m-5 \\ (l-7)+(m-7)=3\end{array}\right. \newline(D) {l−7=(m−7)+5l+m=31 \left\{\begin{array}{l}l-7=(m-7)+5 \\ l+m=31\end{array}\right.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Is (x, y) a solution to the system of equations?right chevron icon

Full solution

Q. Lindsay is 55 years younger than Mark. Seven years ago, the sum of their ages was 3131 .\newlineLet l l be Lindsay's age and let m m be Mark's age.\newlineWhich system of equations represents this situation?\newlineChoose 11 answer:\newline(A) {l=m+5(l−7)+(m−7)=3 \left\{\begin{array}{l}l=m+5 \\ (l-7)+(m-7)=3\end{array}\right. \newline(B) {l−7=(m−7)−5l+m=31 \left\{\begin{array}{l}l-7=(m-7)-5 \\ l+m=31\end{array}\right. \newline(C) {l=m−5(l−7)+(m−7)=3 \left\{\begin{array}{l}l=m-5 \\ (l-7)+(m-7)=3\end{array}\right. \newline(D) {l−7=(m−7)+5l+m=31 \left\{\begin{array}{l}l-7=(m-7)+5 \\ l+m=31\end{array}\right.
  1. Define Variables: Let's define the variables based on the information given:\newlineLet ll be Lindsay's current age.\newlineLet mm be Mark's current age.\newlineWe are told Lindsay is 55 years younger than Mark, which gives us the equation:\newlinel=m−5l = m - 5
  2. Represent Ages Seven Years Ago: Next, we need to represent the information about their ages seven years ago. Seven years ago, Lindsay's age would be l−7l - 7 and Mark's age would be m−7m - 7. The sum of their ages at that time was 3131, so we have the equation:\newline(l−7)+(m−7)=31(l - 7) + (m - 7) = 31
  3. Simplify Equation: Now, let's simplify the second equation:\newlinel−7+m−7=31l - 7 + m - 7 = 31\newlinel+m−14=31l + m - 14 = 31\newlinel+m=31+14l + m = 31 + 14\newlinel+m=45l + m = 45
  4. Form System of Equations: We have two equations now:\newline11. l=m−5l = m - 5\newline22. l+m=45l + m = 45\newlineThis system of equations represents the situation given in the problem. Let's match this system with the answer choices.
  5. Match with Answer Choices: Comparing our system of equations with the answer choices, we find that:\newlineChoice (C) {l=m−5,(l−7)+(m−7)=31}\{l = m - 5, (l - 7) + (m - 7) = 31\} matches our system of equations.

More problems from Is (x, y) a solution to the system of equations?

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

Posted 10 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 10 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 10 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 10 months ago

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

Posted 1 year 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 1 year 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 10 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 10 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 10 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 10 months ago

View all (74)

Related topics

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