usebthe elimination method to solve the following system of equations
4x+y=13
5x-y=5
Answers
Answer:
x = -2, y = 21
Step-by-step explanation:
Let 4x + y = 13 to be equation1 {eqn1}
and let 5x - y = 5 to be equation2 {eqn2}
Using elimination method, you would try to make sure a particular unknown has the same value in both equation 1 and 2. This would make it easy for you to subtract one equation from the other.
Notice how the value of y is the same in both equations. That's a good sign.
But the signs aren't the same. Meaning y in eqn1 has a value of +1, and y in eqn2 has a value of -1. We need to make them similar.
So, we multiply the value of y in eqn1 by all the terms in eqn2. And, do pretty much the same thing by multiplying the value of y in eqn2 by all the terms in eqn1.
You would have:
-1 * (4x + y = 13)
+1 * (5x - y = 5)
This would result in;
-4x - y = -13 (eqn3)
5x - y = 5 (eqn4)
So, just subtract eqn3 from 4
You would have;
(5x - -4x) + (-y -- y) = (-13 - 5)
9x + 0 = -18
x = -18/9 = -2
and to find y;
just substitute the value of x into any of the 4 equations. let's try equation 1
Therefore;
4(-2) + y = 13
-8 + y = 13
y = 13 + 8 = 21
Related Questions
A baseball diamond is a square with a side length of 90 ft. What is the distance from first base to third base in simplest radical form?
Answers
Answer:
90[tex]\sqrt{2}[/tex] ft.
Step-by-step explanation:
Using the Pythagorean theorem we get 90^2 + 90^2 = d^2 where d is the distance from 1st base to third base. So, d^2 = 8100 + 8100 = 16200
d = [tex]\sqrt{16200}[/tex] = 90[tex]\sqrt{2}[/tex]. An easier way to do this is to recognize that the triangle formed by the diagonal of the baseball diamond and the two base paths from home to first and third is a 45-45-90 triangle. Therefore, the hypontenuse (diagonal) equals [tex]\sqrt{2}[/tex] times a leg (90 ft.)
You bought a two liter container of cooking oil for $2.50. What is the cost per liter?
Answers
Answer:
$1.25
Step-by-step explanation:
$2.50 / 2 = $1.25 per liter
Answer:
$1.25
Step-by-step explanation:
.25 + .25= .50
$1.00 + $1.00 = $2.00
$2.00 + .50 = $2.50
Use this table to answer questions below. Choose the correct answer.
According to the line graph, between 1950 and 1970 approximately which year had the lowest percentage of business failures?
Answers
Answer:
The answer is 1954
Step-by-step explanation:
Answer:
1954
Step-by-step explanation:
It is the lowest percentage of business failures. Refer to the scale on the left.
Solve this simultaneous equations: picture below
Answers
Answer:
x = p/11, y = 13p/11
Step-by-step explanation:
The value of x is p/11
The value of y is 13p/11
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 9 is an equation.
We have,
5x + 3y = 4p _____(1)
y = 2x + p ____(2)
Substituting (2) in (1) we get,
5x + 3(2x + p) = 4p
5x + 6x + 3p = 4p
11x = p
x = p/11
Now,
y = 2x + p
y = 2(p/11) + p
y = 2p/11 + p
y = 13p/11
Thus,
x is p/11
y is 13p/11
Learn more about equations here:
https://brainly.com/question/17194269
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over a period of 3 hours, the outside temperature changed an average of -2.25 fahrenheit per hour. select the correct sentence that represents this situation.
the temperature decreased by 2.25 degrees fahrenheit from the beginning to the end of the 3-hour period.
the temperature increased by 0.75 degrees fahrenheit from the beginning to the end of the 3-hour period.
the temperature increased by 6.75 degrees fahrenheit from the beginning to the end of the 3-hour period.
the temperature decreased by 6.75 degrees fahrenheit from the beginning to the end of the 3-hour period.
Answers
Answer:
D
Step-by-step explanation:
-2.25 x 3 = 6.75
the temperature decreased by 6.75 after 3 hours
Answer:
The temperature decreased by 6.75 degrees Fahrenheit.
Step-by-step explanation:
This is answer choice D because the Start of Temperature is:
70F
Start Time: 9AM
(70,9) --> (67.75,10) --> (67.50,11) --> (67.25, 12)
Solve for x and y
Pls help I will give a brainliest to who gets it right
Answers
Answer:
Step-by-step explanation:
(6y-5)+(10y-41)+(12x+22)=180
16y+12x-24=180
16y+12x=204
y=12.75
x=17
A bass guitarist worked on 15 music projects last year. He wrote and produced 5 projects. He wrote a total of 9 projects. Use a Venn diagram to determine:
a. How many projects he wrote but did not produce
b. How many projects he produced but did not write.
Let W be the set of projects the bass guitarist wrote and P be the set of projects he produced
Answers
Step-by-step explanation:
W = Set of projects the guitarist wrote
P = Set of products he produced
A bass guitarist worked on 15 music projects last year.
Universal set = 15
He wrote and produced 5 projects.
W ∩ P = 5
He wrote a total of 9 projects.
W = 9
The Venn Diagram is given in the attached image.
a. How many projects he wrote but did not produce (W - P)?
W - P = W - W ∩ P
W - P = 9 - 5 = 4
He wrote 4 projects but did not produce them.
b. How many projects he produced but did not write (P - W)?
Universal set = (W - P) + (P - W) + W ∩ P
15 = 4 + (P - W) + 5
(P - W) = 15 - 9 = 6
He produced 6 projects but did not write them
HI, i have to turn this in by the end of the day! please help.
Answers
Answer:
Both are 77
Step-by-step explanation:
103 + 103 = 206
360 - 206 = 154
154/2 = 77
#2=77
#4=77
#3 is the same as #1, then subtract them from 360, divide that and you get 77 for the last two.
HELP PLEASE
A rolling pin is shaped like a cylinder with a diameter of 3 inches and a height of 12 inches. How many square inches of space does the rolling pin come in contact with after one complete roll?
Answers
Answer:
[tex]A = 127.17[/tex] square inch
Step-by-step explanation:
Square inches of space covered by rolling pin after one complete roll is equal to the outer surface area of cylinder.
As we know,
Surface area of Cylinder [tex]A=2\pi rh+2\pi r^2\\[/tex]
Substituting the given values in above equation, we get -
[tex]A = (2*3.14*1.5*12) + (2 * 3.14*1.5^2)\\A = 113.04 + 14.13\\A = 127.17[/tex]
[tex]A = 127.17[/tex] square inch
Answer:that’s wrong
Step-by-step explanation:
The car vacuum cleaner at a gas station near Gina’s house costs $0.25 a minute to operate. Gina has $3.25 to spend on vacuuming her car. What is the maximum number of minutes Gina can use the vacuum cleaner?
Answers
Answer:
13 min
Step-by-step explanation:
3.25/0.25=13
Answer:
Gina has 13 minutes to use the vacuum cleaner.
Step-by-step explanation:
3.25/.25= 13 minutes
if time is 9:40, what time would it be in 3/4 hours
Answers
Answer:
10:25
Step-by-step explanation:
3/4 hours = 45 minutes
9:40 to 10:00 is 20 minutes
add another 25 minutes and you get 10:25
what is-56 divided by +7 ?
Answers
Answer:
-8
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
A. x= 3, y= -2
Step-by-step explanation:
[2] 2x= 4y+14
[1] 3y+5x=9
Solve equation [2] for the variable x
[2] 2x = 4y + 14
[2] x = 2y + 7
// Plug this in for variable x in equation [1]
[1] 5•(2y+7) + 3y = 9
[1] 13y = -26
// Solve equation [1] for the variable y
[1] 13y = - 26
[1] y = - 2
// By now we know this much :
x = 2y+7
y = -2
// Use the y value to solve for x
x = 2(-2)+7 = 3
good luck, I hope this helps!!!
Evaluate 3x2 – 3y3 when = 4 and y = 3
Answers
Answer:
24 - 27 (answer would be -3)
Step-by-step explanation:
help please please please please
Answers
Answer:
sorry it's blurry I can't fix it
Which type of interest will earn you more money in a savings account?
Answers
Answer:
a compound interest that has the lowest interest rate .
Step-by-step explanation:
(2+2+2):2•6•2. What is (2+2+2)divided by2•6•2. I no you do the parentheses first them multiple then add I think I still get wrong answer can you help
Answers
Answer: 144
Step-by-step explanation: (2+2+2)(2)(6)(2)
Can anyone help me plz
Answers
Answer:
11
Step-by-step explanation:
BRAINLIEST PLZ
f(2) = (3x2) + 5
= 6+5 = 11
There were 26 people at Charlotte and Oliver's birthday party. The total cost of the party was $1,429.74. How much did each person who attended the party cost?
Answers
Answer:
$54.99/person
Step-by-step explanation:
Divide '26 persons' into the total cost $1,429.74: we get $54.99/person.
Charles has $54.50 saved. He will save $33.25 each week for 30 weeks. How much money will Charles have after 30 weeks?
Answers
Answer:
The answer is
1052
Answer:
Charles will have $1,052 after 30 weeks
Step-by-step explanation:
Charles has $54.50 saved.
He plans to save $33.25 each week.
This means that the first week he will have $54.50 + $33.25 = $87.75
When 30 weeks have passed, he will have:
$54.50 + $33.25 * 30 = $54.50 + $997.50 = $1,052
Charles will have $1,052 after 30 weeks
Aisha harvests 27.5 pounds of tomatoes. She sells 16.92 pounds of the tomatoes at the farmers market. How many pounds of tomatoes does Aisha have left?
Answers
Answer:
10.58
Step-by-step explanation:
27.5 - 16.92= 10.58
HELP! Below is the graph of a polynomial. Which statement about this graph is true?
A. The point (-2,1) is a maximum
B. The point (5,0) is an extreme
C. The point (2,-1.12) is a minimum
D. The point (2,-1.12) is a maximum
Answers
There are 600 members of a sports club.
The ratio of men to women is 2:3
1/4 of the men are under 30 years old
20% of the women are under 30 years old
HOW MANY MEMBERS ARE OVER 30?
Answers
9514 1404 393
Answer:
468
Step-by-step explanation:
Men:
(3/4)(2/5)(600) = (6/20)(600) = 6(30) = 180 men over 30
Women:
(4/5)(3/5)(600) = (12/25)(600) = 48(6) = 288 women over 30
The total number of members over 30 is ...
180 +288 = 468 . . . members over 30
5.5 is what percent of 6.875?
Answers
Answer:
80%
Step-by-step explanation:
11. Twyla and Tony have a 30/5 balloon mortgage for $389,900 with a rate of 4.85%. How much will they pay in interest over the life of the loan? (3 points)
O $81,373.41
$92,263.82
O $107,536.50
O $121,390.73
Answers
Answer:
Explanation:
Twyla and Tony with a balloon mortgage of 30/5 will make constant payments over the space of 5 years and then complete the bulk balloon payment for 25 years remaining.
Given mortgage loan value of $389900
Interest rate of 4.85%
We are asked to calculate the interest over the life of the loan.
We will calculate interest by calculating constant payments over the period of 5 years before balloon payment is due and adding them together then subtracting the mortgage loan given $389900
Formula for constant payments :
A= P×r×r(1+r)^n/(1+r)^n-1
Where A= constant/monthly payments
r= interest rate on the mortgage loan
n= number of payments = 30×12= 360
P= mortgage loan given
A= $389900×0.0485×0.0485(1+0.0485)^360/(1+0.0485)^360-1
=$389900×0.0485×1231340.79/25388468.94
=$389900×0.0485×0.04850
A= $917.142
Payment for five years(with interest)= $917.142×60= $55028.52
Calculate balloon payment:
FV= PV(1+r)^n - P((1+r)^n-1/r)
Where FV= future value of balloon payment
PV= initial loan given
r= interest rate on loan
n= number of payments
P= monthly payments
Substitute:
FV= $389900(1+0.0485/12)^60-917.142((1+0.0485/12)^60-1/0.0485/12)
=$389900×1.2738-917.142(0.2738/0.004041)
=$389900×1.2738-917.142×67.756
= 496654.62-62141.87
FV = $434512.75
Therefore total payment made with interest over the life of the loan= balloon payment+ constant payments for five years= $434512.75+$55028.52
=
5(2a - 6) + 3a
The answer is 13a - 30 right?
Answers
Step-by-step explanation:
5(2a - 6) + 3a
10a - 30 + 3a
13a - 30
right
please answer this correctly without making mistakes
Multiply. Write your answer using the smallest numbers possible.
6 pints 1 cup times 1,156
= pints cups
Answers
Answer:
7514 pints
Step-by-step explanation:
If it is american pints/cups(one pint is two cups)
1. Multiply
6 x 2 = 12
2. Add
12 + 1 = 13
3. Multiply
13 x 1156 = 15028
4. Divide.
15028 divided by 2 = 7514
4x+32=24
show your work
Answers
Answer:
x = -2
Step-by-step explanation:
Original equation:
4x + 32 = 24
Subtract 32 from 24
-8
The equation should look like this now:
4x = -8
Divide both sides by 4
x = -2
Hope this helps :)
Select all the equations that represent this situation. Diego has run 2/3 of a race's
distance. He has run 8 & 1/2 kilometers. How long is the whole race?
8 & 1/2 divided by 2/3 = ?
2/3 divided by 8 & 1/2 = ?
2/3 x ? = 8 & 1/2
8 & 1/2 x ? = 2/3
8 & 1/2 times 3/2 = ?
8 & 1/2 x 2/3 = ?
Answers
Step-by-step explanation:
Diego has run 2/3 of a race's
Let total distance of the race = y
He has run 8 & 1/2 kilometers.
This means 2/3 of y = 8 & 1/2 km
How long is the whole race?
2 / 3 x y = 8 & 1/2
The following equations can be used to calculate the distance of the whole race;
8 & 1/2 divided by 2/3 = ?
2/3 x ? = 8 & 1/2
8 & 1/2 times 3/2 = ?
If gas costs $5.09 per gallon, how many whole gallons of gas could you buy with $54.00?
(Make sure to answer with a whole number.)
Answers
Answer:
10 gallons!
Step-by-step explanation:
Please mark me brainliest!!
Answer:
10 gallons
Step-by-step explanation: