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romanna [79]
2 years ago
12

The sum of four times a number and five times another number is -28. The sum of nine times the first number and two times the se

cond number is 11
Mathematics
1 answer:
Rina8888 [55]2 years ago
3 0

Answer:

<h2>3 and -8</h2>

Step-by-step explanation:

x,\ y-the\ numbers\\\\\text{The sum of four times a number and five times another number is -28:}\\\\4x+5y=-28\\\\\text{The sum of nine times the first number and two times the second number is 11:}\\\\9x+2y=11\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}4x+5y=-28&\text{multiply both sides by2}\\9x+2y=11&\text{multiply both sides by (-5)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}8x+10y=-56\\-45x-10y=-55\end{array}\right}\qquad\text{add both sides of the equation}

.\qquad-37x=-111\qquad\text{divide both sides by (-37)}\\.\qquad\qquad\boxed{x=3}\\\\\text{Put the value of x to the first equation:}\\\\4(3)+5y=-28\\12+5y=-28\qquad\text{subtrac 12 from both sides}\\5y=-40\qquad\text{divide both sides by 5}\\\boxed{y=-8}

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Step-by-step explanation:

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gallons of water can fill a pool that is 50 yards by 20 yards and is 9 feet deep? (Assume 7 1/2 gallons per cubic foot.)
saul85 [17]
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4 0
2 years ago
14.What is the solution of the system?
Archy [21]

Answer:

14.  x=-2.5,  y = -7

15.  x=28  y = -20

Step-by-step explanation:

14.  Let's solve this system by elimination.  Multiply the first equation by -1.

-1*(4x-y)= -1*(- 3)

-4x +y = 3

Then add this to the second equation.

-4x+y = 3

6x-y= - 8

--------------

2x   = -5


Divide each side by 2

x = -2.5

We still need to find y

-4x+y =3

-4(-2.5) + y =3

10 +y =3

Subtract 10 from each side.

y = 3-10

y = -7


15.I will again use elimination to solve this system, because using substitution will give me fractions which are harder to work with.   I will elimiate the y variable.  Multiply the first equation by 11

11( 5x+6y)= 11*20

55x+66y = 220

Multiply the second equation by -6

-6(9x+11y)=32*(-6)

-54x-66y = -192


Add the modified equations together.

55x+66y = 220

-54x-66y = -192

---------------------------

x = 28

We still need to solve for y

5x+6y = 20

5*28 + 6y =20

140 + 6y = 20

Subtract 140 from each side

6y = -120

Divide by 6

y = -20

3 0
2 years ago
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