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

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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.

Aziza is solving this equation-2(1+x)=4x+10
No. 3^32 -1 has exactly two divisors greater than 75 and less than 85 what is their product?
x^2+7x-19=0 has Two solutions A and B give your answer to 3 decimal places
3. When Jenna spent 10 minutes on the elliptical trainer and then did circuit training for20 minutes, her fitness app says she burned 278 calories. When she spent 20 minutes onthe elliptical trainer and 30 minutes circuit training she burned 473 calories. How manycalories does she burn for each minute on the elliptical trainer? How many calories doesshe burn for each minute of circuit training?
.473
Angelita
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Angelita
John left his house in Irvine at 8:35 am to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50. At 3:30 pm, he left the meeting and drove home. He arrived home at 5:18.
p-2/3=5/6 how do I solve it with explanation pls
P=3/2
Vanarith
1/2p2-2/3p=5p/6
James
Cindy
4.5
Ruth
is y=7/5 a solution of 5y+3=10y-4
yes
James
Cindy
Lucinda has a pocketful of dimes and quarters with a value of $6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does Lucinda have? Rhonda Reply Find an equation for the line that passes through the point P ( 0 , − 4 ) and has a slope 8/9 . Gabriel Reply is that a negative 4 or positive 4? Felix y = mx + b Felix if negative -4, then -4=8/9(0) + b Felix -4=b Felix if positive 4, then 4=b Felix then plug in y=8/9x - 4 or y=8/9x+4 Felix Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. macadamia nuts cost$9 per pound and almonds cost $5.25 per pound. how many pounds of macadamia nuts and how many pounds of almonds should macario use for the mixture to cost$6.50 per pound to make?
Nga and Lauren bought a chest at a flea market for $50. They re-finished it and then added a 350 % mark - up Makaila Reply$1750
Cindy
the sum of two Numbers is 19 and their difference is 15
2, 17
Jose
interesting
saw
4,2
Cindy
Felecia left her home to visit her daughter, driving 45mph. Her husband waited for the dog sitter to arrive and left home 20 minutes, or 13 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?
hola saben como aser un valor de la expresión
NAILEA
integer greater than 2 and less than 12
2 < x < 12
Felix
I'm guessing you are doing inequalities...
Felix
Actually, translating words into algebraic expressions / equations...
Felix
hi
Darianna
hello
Mister
Eric here
Eric
6
Cindy