# 5.3 Solve systems of equations by elimination  (Page 4/6)

 Page 4 / 6

The sum of two numbers is 39. Their difference is 9. Find the numbers.

## Solution

$\begin{array}{ccc}\mathbf{\text{Step 1. Read}}\phantom{\rule{0.2em}{0ex}}\text{the problem}\hfill & & \\ \mathbf{\text{Step 2. Identify}}\phantom{\rule{0.2em}{0ex}}\text{what we are looking for.}\hfill & & \hfill \text{We are looking for two numbers.}\hfill \\ \mathbf{\text{Step 3. Name}}\phantom{\rule{0.2em}{0ex}}\text{what we are looking for.}\hfill & & \begin{array}{c}\hfill \text{Let}\phantom{\rule{0.2em}{0ex}}n=\phantom{\rule{0.2em}{0ex}}\text{the first number.}\hfill \\ \hfill \phantom{\rule{2.3em}{0ex}}m=\text{the second number}\hfill \end{array}\hfill \\ \begin{array}{c}\mathbf{\text{Step 4. Translate}}\phantom{\rule{0.2em}{0ex}}\text{into a system of equations.}\hfill \\ \\ \\ \\ \\ \\ \\ \end{array}\hfill & & \hfill \begin{array}{}\\ \text{The sum of two numbers is 39.}\hfill \\ \hfill \phantom{\rule{0.3em}{0ex}}n+m=39\hfill \\ \hfill \text{Their difference is 9.}\hfill \\ \hfill n-m=9\hfill \end{array}\hfill \\ \text{The system is:}\hfill & & \hfill \left\{\begin{array}{c}n+m=39\hfill \\ n-m=9\hfill \end{array}\hfill \\ \begin{array}{c}\mathbf{\text{Step 5. Solve}}\phantom{\rule{0.2em}{0ex}}\text{the system of equations.}\hfill \\ \text{To solve the system of equations, use}\hfill \\ \text{elimination. The equations are in standard}\hfill \\ \text{form and the coefficients of}\phantom{\rule{0.2em}{0ex}}m\phantom{\rule{0.2em}{0ex}}\text{are}\hfill \\ \text{opposites. Add.}\hfill \\ \\ \text{Solve for}\phantom{\rule{0.2em}{0ex}}n.\hfill \\ \\ \\ \\ \\ \end{array}\hfill & & \hfill \begin{array}{c}\hfill \underset{\text{____________}}{\left\{\begin{array}{c}n+m=39\hfill \\ n-m=9\hfill \end{array}}\hfill \\ \hfill 2n\phantom{\rule{1.8em}{0ex}}=48\hfill \\ \\ \hfill \phantom{\rule{2.21em}{0ex}}n=24\hfill \end{array}\hfill \\ \begin{array}{c}\text{Substitute}\phantom{\rule{0.2em}{0ex}}n=24\phantom{\rule{0.2em}{0ex}}\text{into one of the original}\hfill \\ \text{equations and solve for}\phantom{\rule{0.2em}{0ex}}m.\hfill \end{array}\hfill & & \hfill \begin{array}{c}\hfill \phantom{\rule{0.2em}{0ex}}\begin{array}{c}\hfill n+m=39\\ \hfill 24+m=39\\ \hfill m=15\end{array}\hfill \end{array}\hfill \\ \mathbf{\text{Step 6. Check}}\phantom{\rule{0.2em}{0ex}}\text{the answer.}\hfill & & \phantom{\rule{1.55em}{0ex}}\text{Since}\phantom{\rule{0.2em}{0ex}}24+15=39\phantom{\rule{0.2em}{0ex}}\text{and}\hfill \\ & & \hfill 24-15=9,\phantom{\rule{0.2em}{0ex}}\text{the answers check.}\hfill \\ \mathbf{\text{Step 7. Answer}}\phantom{\rule{0.2em}{0ex}}\text{the question.}\hfill & & \hfill \text{The numbers are 24 and 15.}\hfill \end{array}$

The sum of two numbers is 42. Their difference is 8. Find the numbers.

The numbers are 25 and 17.

The sum of two numbers is −15. Their difference is −35. Find the numbers.

The numbers are −25 and 10.

Joe stops at a burger restaurant every day on his way to work. Monday he had one order of medium fries and two small sodas, which had a total of 620 calories. Tuesday he had two orders of medium fries and one small soda, for a total of 820 calories. How many calories are there in one order of medium fries? How many calories in one small soda?

## Solution

 Step 1. Read the problem. Step 2. Identify what we are looking for. We are looking for the number of calories in one order of medium fries and in one small soda. Step 3. Name what we are looking for. Let f = the number of calories in 1 order of medium fries.     s = the number of calories in 1 small soda. Step 4. Translate into a system of equations: one medium fries and two small sodas had a total of 620 calories two medium fries and one small soda had a total of 820 calories. Our system is: Step 5. Solve the system of equations. To solve the system of equations, use elimination. The equations are in standard form. To get opposite coefficients of f , multiply the top equation by −2. Simplify and add. Solve for s . Substitute s = 140 into one of the original equations and then solve for f . Step 6. Check the answer. Verify that these numbers make sense in the problem and that they are solutions to both equations. We leave this to you! Step 7. Answer the question. The small soda has 140 calories and the fries have 340 calories.

Malik stops at the grocery store to buy a bag of diapers and 2 cans of formula. He spends a total of $37. The next week he stops and buys 2 bags of diapers and 5 cans of formula for a total of$87. How much does a bag of diapers cost? How much is one can of formula?

The bag of diapers costs $11 and the can of formula costs$13.

To get her daily intake of fruit for the day, Sasha eats a banana and 8 strawberries on Wednesday for a calorie count of 145. On the following Wednesday, she eats two bananas and 5 strawberries for a total of 235 calories for the fruit. How many calories are there in a banana? How many calories are in a strawberry?

There are 105 calories in a banana and 5 calories in a strawberry.

(a+b)(p+q+r)(b+c)(p+q+r)(c+a) (p+q+r)
4x-7y=8 2x-7y=1 what is the answer?
x=7/2 & y=6/7
Pbp
x=7/2 & y=6/7 use Elimination
Debra
true
bismark
factoriz e
usman
4x-7y=8 X=7/4y+2 and 2x-7y=1 x=7/2y+1/2
Peggie
Frank
thanks
Ramil
copy and complete the table. x. 5. 8. 12. then 9x-5. to the 2nd power+4. then 2xto the second power +3x
What is c+4=8
2
Letha
4
Lolita
4
Rich
4
thinking
C+4=8 -4 -4 C =4
thinking
I need to study
Letha
4+4=8
William
During two years in college, a student earned $9,500. The second year, she earned$500 more than twice the amount she earned the first year.
9500=500+2x
Debra
9500-500=9000 9000÷2×=4500 X=4500
Debra
X + Y = 9500....... & Y = 500 + 2X so.... X + 500 + 2X = 9500, them X = 3000 & Y = 6500
Pbp
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles.
Reiko needs to mail her Christmas cards and packages and wants to keep her mailing costs to no more than $500. The number of cards is at least 4 more than twice the number of packages. The cost of mailing a card (with pictures enclosed) is$3 and for a package the cost is $7. Ida Reply hey Juan Sup patrick The sum of two numbers is 155. The difference is 23. Find the numbers Michelle Reply The sum of two numbers is 155. Their difference is 23. Find the numbers Michelle The difference between 89 and 66 is 23 Ciid Joy is preparing 20 liters of a 25% saline solution. She only has 40% and 10% solution in her lab. How many liters of the 40% and how many liters of the 10% should she mix to make the 25% solution? Amber Reply hello bismark I need a math tutor BAD Stacie Me too Letha me too Xavier ok Bishal teet Bishal Sue and Deb work together writing a book that takes them 90 days. If Sue worked alone, it would take her 120 days. How long would it take Deb to write the book alone? Hailey Reply Tell Deb to write the book alone and report back on how long it took her. Deb could get bored and stop, she could get sick next week and prolong the time, she could die next month. This question is impossible to answer. vV right* tyler is there a thumbs up mathematical symbol in algebra? 👍²= vV 90days x 120days =10800 120days - 90days = 30 10800days/30days= 360days? (ad) derall=1440 mins (90x ad )+(120 x ad )/(120 x ad ))-((90d x ad)= you go glen coco! I'll see my self out Nick Larry and Tom were standing next to each other in the backyard when Tom challenged Larry to guess how tall he was. Larry knew his own height is 6.5 feet and when they measured their shadows, Larry’s shadow was 8 feet and Tom’s was 7.75 feet long. What is Tom’s height? genevieve Reply 6.25 Ciid 6.25 Big ? Twila Wayne is hanging a string of lights 57 feet long around the three sides of his patio, which is adjacent to his house. the length of his patio, the side along the house, is 5 feet longer than twice it's width. Find the length and width of the patio. Katherine Reply complexed. could you please help me figure out? Ciid (sin=opp/adj) (tan= opp/adj) cos=hyp/adj tyler (sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up tyler (sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up tyler (sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up tyler SOH = Sine is Opposite over Hypotenuse. CAH= Cosine is Adjacent over Hypotenuse. TOA = Tangent is Opposite over Adjacent. tyler H=57 and O=285 figure out what the adjacent? tyler help Twila draw a diagram first John Amara currently sells televisions for company A at a salary of$17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of$29,000 plus a \$20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
what is the quantity and price of the televisions for both options?
karl
Amara has to sell 120 televisions to make 29,000 of the salary of company B. 120 * TV 100= commission 12,000+ 17,000 = of company a salary 29,000 17000+
Ciid
Amara has to sell 120 televisions to make 29,000 of the salary of company B. 120 * TV 100= commission 12,000+ 17,000 = of company a salary 29,000
Ciid
I'm mathematics teacher from highly recognized university.
here a question professor How many soldiers are there in a group of 27 sailors and soldiers if there are four fifths as many sailors as soldiers? can you write out the college you went to with the name of the school you teach at and let me know the answer I've got it to be honest with you
tyler
is anyone else having issues with the links not doing anything?
Yes
Val