Mathematics, 15.07.2019 14:30 krojas015

Did you hear about the big that built himself a home ? it’s a riddle i need to solve for algebra! pls !

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Answer from: lonelynomad00

Part a)

3x+2y=12> equation 1

y=x-9> equation 2

substitute equation 2 in equation 1

3x+2*[x-9]=12> 3x+2x-18=12> 5x=30> x=6

y=6-9> y=-3

the answer part a) is

(6,-3)> word> HE

Part b)

4x+y=-2> equation 1

y=2x-2> equation 2

substitute equation 2 in equation 1

4x+[2x-2]=-2> 6x=0> x=0

y=2*0-2> y=-2

the answer part b) is

(0,-2)> word> MADE

Part c)

-3x+5y=5> equation 1

y=x-1> equation 2

substitute equation 2 in equation 1

-3x+5*[x-1]=5> -3x+5x-5=5> 2x=10> x=5

y=5-1> y=4

the answer Part c) is

(5,4)> word> A

Part d)

2x+y=-16> equation 1

y=2x---> equation 2

substitute equation 2 in equation 1

2x+[2x]=-16> 4x=-16> x=-4

y=2*(-4)> y=-8

the answer Part d) is

(-4,-8)> word> KNOT

Part e)

7x=-35> x=-5

-8x+9y=4> -8*(-5)+9y=4> 40+9y=4> 9y=-36> y=-4

the answer Part e) is

(-5,-4)> word> IN

Part f)

-4x+3y=20> equation 1

-14y=-56> y=4

substitute in equation 1

-4x+3*4=20> -4x=8> x=-2

the answer Part f) is

(-2,4)> word> HIS

Part g)

13x-6y=-5> equation 1

x+10=11> x=1

13*1-6y=-5> -6y=-5-13> y=3

the answer Part g) is

(1,3)> word> TAIL

Part h)

9x-2y=12> equation 1

y+4=16> y=12

9x-2*12=12> 9x=36> x=4

the answer Part h) is

(4,12)> word> AND

Part i)

x=6+2y> equation 1

-3x+14y=-18> equation 2

substitute equation 1 in equation 2

-3*[6+2y]+14y=-18> -18-6y+14y=-18> 8y=0> y=0

x=6+2*0> x=6

the answer Part i) is

(6,0)> word> CALLED

Part j)

5x-9y=12> equation 1

y=-6-x> equation 2

substitute equation 2 in equation 1

5x-9*[-6-x]=12> 5x+54+9x=12> 14x=-42> x=-3

y=6-(-3)> y=-3

the answer Part j) is

(-3,-3)> word> IT

Part k)

x=-8+y> equation 1

6x+y=-6> equation 2

substitute equation 1 in equation 2

6*[-8+y]+y=-6> -48+6y+y=-6> 7y=42> y=6

x=-8+6> x=-2

the answer Part k) is

(-2,6)> word> A

Part l)

7x-3y=17> equation 1

y=2x-6> equation 2

substitute equation 2 in equation 1

7x-3*[2x-6]=17> 7x-6x+18=17> x=-1

y=2*(-1)-6> y=-8

the answer Part l) is

(-1,-8)> word> PIGS

part m)

The physical education instructor asked each student to do a total of 36 pull-ups and push-ups in 1 minute. The instructor wanted students to do 8 times as many push-ups as pull-ups. Write a system of linear equations that represents this situation. How many pull-ups and push-ups were required in 1 minute?

let

x>pull-ups

y>push-ups

we know that
x+y=36> equation 1
y=8x> equation 2
substitute equation 2 in equation 1
x+8x=36> 9x=36> x=4
y=8*4> y=32
the solution is (4.32)> word TIE

HE MADE A KNOT IN HIS TAIL AND CALLED IT A PIG'S TIE

Answer from: mismhan01

By solving the systems of linear equations given by substitution, the riddle solved is: HE MADE A KNOT IN HIS TAIL AND CALLED IT A PIG'S TIE

To solve the riddle, the following systems of linear equations would be solved by finding the values of x and y by substitution:

A. 3x + 2y = 12 --> Eqn. 1

y = x - 9 --> Eqn. 2

Substitute y = x - 9 into eqn. 1 to find x

$3x + 2(x - 9) = 12\\3x + 2x - 18 = 12\\5x - 18 = 12\\5x = 12 + 18\\5x = 30\\x = 6$

Substitute x = 6 into eqn. 2 to find y

$y = 6 - 9\\y = -3$

The solution is (6, -3) which tallies with the word: HE

B. 4x + y = -2 --> Eqn. 1

y = 2x - 2 --> Eqn. 2

Substitute y = 2x - 2 into eqn. 1 to find x

$4x + 2x - 2 = -2\\6x - 2 = -2\\6x = -2 + 2\\6x = 0\\x = 0$

Substitute x = 0 into eqn. 2 to find y

$y = 2(0) - 2 \\y = 0 - 2\\y = -2$

The solution is (0, -2) which tallies with the word: MADE

C. -3x + 5y = 5 --> Eqn. 1

y = x - 1 --> Eqn. 2

Substitute y = x - 1 into eqn. 1 to find x

$-3x + 5(x - 1) = 5\\-3x + 5x - 5 = 5\\2x - 5 = 5\\2x = 5 + 5\\2x = 10\\x = 5$

Substitute x = 5 into eqn. 2 to find y

$y = 5 - 1\\y = 4$

The solution is (5, 4) which tallies with the word: A

D. 2x + y = -16 --> Eqn. 1

y = 2x --> Eqn. 2

Substitute y = 2x into eqn. 1 to find x

$2x + 2x = -16\\4x = -16\\x = -4$

Substitute x = -4 into eqn. 2 to find y

$y = 2(-4)\\y = -8$

The solution is (-4, -8) which tallies with the word: KNOT

E. 7x = -35 --> Eqn. 1

-8x + 9y = 4 --> Eqn. 2

Solve eqn. 1. to find x

$7x = -35\\x = -5$

Substitute x = -5 into eqn. 2 to find y

$-8(-5) + 9y = 4\\40 + 9y = 4\\9y = 4 - 40\\9y = -36\\y = -4$

The solution is (-5, -4) which tallies with the word: IN

F. -4x + 3y = 20 --> Eqn. 1

-14y = -56 --> Eqn. 2

Solve eqn. 2 to find y

$-14y = -56\\y = 4$

Substitute y = 4 into eqn. 1 to find y

$-4x + 3(4) = 20\\-4x + 12 = 20\\-4x = 20 - 12\\-4x = 8\\x = -2$

The solution is (-2, 4) which tallies with the word: HIS

G. 13x - 6y = -5 --> Eqn. 1

x + 10 = 11 --> Eqn. 2

Solve eqn. 2 to find x

x = 11 - 10

x = 1

Substitute x = 1 into eqn. 1 to find y

$13(1) - 6y = -5 \\13 - 6y = -5\\-6y = -5 -13\\-6y = -18\\y = 3$

The solution is (1, 3) which tallies with the word: TAIL

i. x = 6 + 2y --> Eqn. 1

-3x + 14y = -18 --> Eqn. 2

Substitute x = 6 + 2y into eqn. 2 to find y

$-3(6 + 2y) + 14y = -18\\-18 - 6y + 14y = -18\\8y = -18 + 18\\8y = 0\\y = 0$

Substitute y = 0 into eqn. 1 to find x

$x = 6 + 2(0)\\x = 6$

The solution is (6, 0) which tallies with the word: CALLED

H. 9x - 2y = 12 --> Eqn. 1

y + 4 = 16 --> Eqn. 2

Solve eqn. 2 to find y

y = 16 - 4

y = 12

Substitute y = 12 into eqn. 1 to find x

$9x - 2(12) = 12\\9x - 24 = 12\\9x = 12 + 24\\9x = 36\\x = 4$

The solution is (4, 12) which tallies with the word: AND

I. x = 6 + 2y --> Eqn. 1

-3x + 14y = -18 --> Eqn. 2

Substitute x = 6 + 2y into eqn. 2 to find y

$-3(6 + 2y) + 14y = -18\\-18 - 6y + 14y = -18\\8y = -18 + 18\\8y = 0\\y = 0$

Substitute y = 0 into eqn. 1 to find x

$x = 6 + 2(0)\\x = 6$

The solution is (6, 0) which tallies with the word: CALLED

J. 5x - 9y = 12 --> Eqn. 1

y = -6 - x --> Eqn. 2

Substitute y = -6 - x into eqn. 1 to find x

$5x - 9(-6 - x) = 12\\5x + 54 + 9x = 12\\14x = 12 - 54\\14x = -42\\x = -3$

Substitute x = -3 into eqn. 2 to find y

$y = -6 - (-3)\\y = -3$

The solution is (-3, -3) which tallies with the word: IT

K. x = -8 + y--> Eqn. 1

6x + y = -6 --> Eqn. 2

Substitute x = -8 + y into eqn. 2 to find y

$6(-8 + y) + y = -6\\-48 + 6y + y = -6\\7y = -6 + 48\\7y = 42\\y = 6$

Substitute y = 6 into eqn. 1 to find x

x = -8 + 6

x = -2

The solution is (-2, 6) which tallies with the word: A

L. 7x - 3y = 17 --> Eqn. 1

y = 2x - 6 --> Eqn. 2

Substitute y = 2x - 6 into eqn. 1 to find x

$7x - 3(2x - 6) = 17\\7x - 6x + 18 = 17\\x = 17 - 18\\x = -1$

Substitute x = -1 into eqn. 2 to find y

$y = 2(-1) - 6\\y = -2 - 6\\y = -8$

The solution is (-1, -8) which tallies with the word: PIGS

M. Given that the total number of push-ups and pull-ups equals 36,

Let,

x = number of push-upsy = number of pull-ups

The first equation that can be formed from this is:

x + y = 36 --> Eqn. 1

Also, if the instructor wants 8 times as many push-ups as pull-ups from the students, we would have the second equation as:

y = 8x --> Eqn. 2

Substitute y = 8x into eqn. 1 to find the value of x

$x + 8x = 36\\\\9x = 36\\\\x = 4$

Number of push-ups in 1 min = 4

Substitute x = 4 into eqn. 2 to find the value of y

$y = 8(4)\\\\y = 32$

Number of push-ups in 1 min = 32

The solution to the system of linear equations would be (4, 32) which corresponds to the word: TIE.

Therefore, by solving the systems of linear equations given by substitution, the riddle solved is: HE MADE A KNOT IN HIS TAIL AND CALLED IT A PIG'S TIE

Learn more here:

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Answer from: Quest

linear

step-by-step explanation:

Answer from: Quest

the answer to question 1 is -8, 28.

step-by-step explanation:

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