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

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$\left\{\begin{array}{c}2x+9y=-4\hfill \\ 3x+13y=-7\hfill \end{array}$

$\left\{\begin{array}{c}\frac{1}{3}x-y=-3\hfill \\ x+\frac{5}{2}y=2\hfill \end{array}$

$\left(-3,2\right)$

$\left\{\begin{array}{c}x+\frac{1}{2}y=\frac{3}{2}\hfill \\ \frac{1}{5}x-\frac{1}{5}y=3\hfill \end{array}$

$\left\{\begin{array}{c}x+\frac{1}{3}y=-1\hfill \\ \frac{1}{2}x-\frac{1}{3}y=-2\hfill \end{array}$

$\left(-2,3\right)$

$\left\{\begin{array}{c}\frac{1}{3}x-y=-3\hfill \\ \frac{2}{3}x+\frac{5}{2}y=3\hfill \end{array}$

$\left\{\begin{array}{c}2x+y=3\hfill \\ 6x+3y=9\hfill \end{array}$

infinitely many solutions

$\left\{\begin{array}{c}x-4y=-1\hfill \\ -3x+12y=3\hfill \end{array}$

$\left\{\begin{array}{c}-3x-y=8\hfill \\ 6x+2y=-16\hfill \end{array}$

infinitely many solutions

$\left\{\begin{array}{c}4x+3y=2\hfill \\ 20x+15y=10\hfill \end{array}$

$\left\{\begin{array}{c}3x+2y=6\hfill \\ -6x-4y=-12\hfill \end{array}$

infinitely many solutions

$\left\{\begin{array}{c}5x-8y=12\hfill \\ 10x-16y=20\hfill \end{array}$

$\left\{\begin{array}{c}-11x+12y=60\hfill \\ -22x+24y=90\hfill \end{array}$

inconsistent, no solution

$\left\{\begin{array}{c}7x-9y=16\hfill \\ -21x+27y=-24\hfill \end{array}$

$\left\{\begin{array}{c}5x-3y=15\hfill \\ y=\frac{5}{3}x-2\hfill \end{array}$

inconsistent, no solution

$\left\{\begin{array}{c}2x+4y=7\hfill \\ y=-\frac{1}{2}x-4\hfill \end{array}$

Solve Applications of Systems of Equations by Elimination

In the following exercises, translate to a system of equations and solve.

The sum of two numbers is 65. Their difference is 25. Find the numbers.

The numbers are 20 and 45.

The sum of two numbers is 37. Their difference is 9. Find the numbers.

The sum of two numbers is −27. Their difference is −59. Find the numbers.

The numbers are 16 and −43.

The sum of two numbers is −45. Their difference is −89. Find the numbers.

Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 2 sweaters for $114 or she is able to buy 2 shirts and 4 sweaters for$164. How much does a shirt cost? How much does a sweater cost?

A shirt costs $16 and a sweater costs$33.

Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40 or he is able to buy 5 packages of paper and 6 staplers for$62. How much does a package of paper cost? How much does a stapler cost?

The total amount of sodium in 2 hot dogs and 3 cups of cottage cheese is 4720 mg. The total amount of sodium in 5 hot dogs and 2 cups of cottage cheese is 6300 mg. How much sodium is in a hot dog? How much sodium is in a cup of cottage cheese?

There are 860 mg in a hot dog. There are 1,000 mg in a cup of cottage cheese.

The total number of calories in 2 hot dogs and 3 cups of cottage cheese is 960 calories. The total number of calories in 5 hot dogs and 2 cups of cottage cheese is 1190 calories. How many calories are in a hot dog? How many calories are in a cup of cottage cheese?

Choose the Most Convenient Method to Solve a System of Linear Equations

In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination.

$\left\{\begin{array}{c}8x-15y=-32\hfill \\ 6x+3y=-5\hfill \end{array}$
$\left\{\begin{array}{c}x=4y-3\hfill \\ 4x-2y=-6\hfill \end{array}$

elimination substitution

$\left\{\begin{array}{c}y=7x-5\hfill \\ 3x-2y=16\hfill \end{array}$
$\left\{\begin{array}{c}12x-5y=-42\hfill \\ 3x+7y=-15\hfill \end{array}$

$\left\{\begin{array}{c}y=4x+9\hfill \\ 5x-2y=-21\hfill \end{array}$
$\left\{\begin{array}{c}9x-4y=24\hfill \\ 3x+5y=-14\hfill \end{array}$

substitution elimination

$\left\{\begin{array}{c}14x-15y=-30\hfill \\ 7x+2y=10\hfill \end{array}$
$\left\{\begin{array}{c}x=9y-11\hfill \\ 2x-7y=-27\hfill \end{array}$

## Everyday math

Norris can row 3 miles upstream against the current in the same amount of time it takes him to row 5 miles downstream, with the current. Solve the system. $\left\{\begin{array}{c}r-c=3\hfill \\ r+c=5\hfill \end{array}$

1. for $r$ , his rowing speed in still water.
2. Then solve for $c$ , the speed of the river current.

$r=4$ $c=1$

Josie wants to make 10 pounds of trail mix using nuts and raisins, and she wants the total cost of the trail mix to be $54. Nuts cost$6 per pound and raisins cost $3 per pound. Solve the system $\left\{\begin{array}{c}n+r=10\hfill \\ 6n+3r=54\hfill \end{array}$ to find $n$ , the number of pounds of nuts, and $r$ , the number of pounds of raisins she should use. ## Writing exercises Solve the system $\left\{\begin{array}{c}x+y=10\hfill \\ 5x+8y=56\hfill \end{array}$ by substitution by graphing Which method do you prefer? Why? 1. (8, 2) 2. Answers will vary. Solve the system $\left\{\begin{array}{c}x+y=-12\hfill \\ y=4-\frac{1}{2}x\hfill \end{array}$ by substitution by graphing Which method do you prefer? Why? ## Self check After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. What does this checklist tell you about your mastery of this section? What steps will you take to improve? #### Questions & Answers hello, I have algebra phobia. Subtracting negative numbers always seem to get me confused. Alicia Reply what do you need help in? Felix subtracting a negative....is adding!! Heather look at the numbers if they have different signs, it's like subtracting....but you keep the sign of the largest number... Felix for example.... -19 + 7.... different signs...subtract.... 12 keep the sign of the "largest" number 19 is bigger than 7.... 19 has the negative sign... Therefore, -12 is your answer... Felix —12 Niazmohammad Thanks Felix.l also get confused with signs. Esther Thank you for this Shatey 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 John Reply 168.50=R Heather john is 5years older than wanjiru.the sum of their years is27years.what is the age of each achol Reply 46 mustee j 17 w 11 Joseph john is 16. wanjiru is 11. Felix 27-5=22 22÷2=11 11+5=16 Joyce where's the answers? Ed Reply I don't see where the answers are. Ed Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart? Maddy Reply 3 Christopher 18t+14t=96 32t=96 32/96 3 Christopher show that a^n-b^2n is divisible by a-b Florence Reply What does 3 times your weight right now Cherokee Reply Use algebra to combine 39×5 and the half sum of travel of 59+30 Cherokee What is the segment of 13? Explain Cherokee my weight is 49. So 3 times is 147 Cherokee kg to lbs you goin to convert 2.2 or one if the same unit your going to time your body weight by 3. example if my body weight is 210lb. what would be my weight if I was 3 times as much in kg. that's you do 210 x3 = 630lb. then 630 x 2.2= .... hope this helps tyler How to convert grams to pounds? paul What is the lcm of 340 Kendra Reply Yes Cherokee How many numbers each equal to y must be taken to make 15xy Malik Reply 15x Martin 15x Asamoah 15x Hugo 1y Tom 1y x 15y Tom find the equation whose roots are 1 and 2 Adda Reply (x - 2)(x -1)=0 so equation is x^2-x+2=0 Ranu I believe it's x^2-3x+2 NerdNamedGerg because the X's multiply by the -2 and the -1 and than combine like terms NerdNamedGerg find the equation whose roots are -1 and 4 Adda Ans = ×^2-3×+2 Gee find the equation whose roots are -2 and -1 Adda (×+1)(×-4) = x^2-3×-4 Gee yeah Asamoah Quadratic equations involving factorization Winner Reply there's a chatting option in the app wow Nana That's cool cool Nana Nice to meet you all Nana you too. Joan 😃 Nana Hey you all there are several Free Apps that can really help you to better solve type Equations. Debra Debra, which apps specifically. ..? Nana am having a course in elementary algebra ,any recommendations ? samuel Samuel Addai, me too at ucc elementary algebra as part of my core subjects in science Nana me too as part of my core subjects in R M E Ken at ABETIFI COLLEGE OF EDUCATION Ken ok great. Good to know. Joan 5x + 1/3= 2x + 1/2 sanam Plz solve this sanam 5x - 3x = 1/2 - 1/3 2x = 1/6 x = 1/12 Ranu Thks ranu sanam Please help me solve this 10x+14=-2x+38 Erica the previous equation should be 3x = 1/6 x=1/18 Sriram for the new one 10x + 2x = 38 - 14 Sriram 12x = 24 x=2 Sriram 10x + 14 = -2x +38 10x + 2x = 38 - 14 12x = 24 divide both sides by the coefficient of x, which is 12 therefore × = 2 vida a trader gains 20 rupees loses 42 rupees and then gains ten rupees Express algebraically the result of his transactions vinaya Reply a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs$6.04 per gallon and the soda costs $4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs$5.71 per gallon?
(a+b)(p+q+r)(b+c)(p+q+r)(c+a) (p+q+r)
really
Asamoah
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
x=7/2 y=6/7
Asamoah
Thanks , all of you are correct.
Joseph