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katrin2010 [14]
3 years ago
5

Solve the system by substitution. [-2.5x+y = 13.5 12.25x - y=-12.25

Mathematics
1 answer:
IrinaK [193]3 years ago
5 0

Answer:

x = 5/39 , y = 539/39

Step-by-step explanation:

Solve the following system:

{y - 2.5 x = 13.5

12.25 x - y = -12.25

In the first equation, look to solve for y:

{y - 2.5 x = 13.5

12.25 x - y = -12.25

y - 2.5 x = y - (5 x)/2 and 13.5 = 27/2:

y - (5 x)/2 = 27/2

Add (5 x)/2 to both sides:

{y = 1/2 (5 x + 27)

12.25 x - y = -12.25

Substitute y = 1/2 (5 x + 27) into the second equation:

{y = 1/2 (5 x + 27)

1/2 (-5 x - 27) + 12.25 x = -12.25

(-5 x - 27)/2 + 12.25 x = 12.25 x + (-(5 x)/2 - 27/2) = 9.75 x - 27/2:

{y = 1/2 (5 x + 27)

9.75 x - 27/2 = -12.25

In the second equation, look to solve for x:

{y = 1/2 (5 x + 27)

9.75 x - 27/2 = -12.25

9.75 x - 27/2 = (39 x)/4 - 27/2 and -12.25 = -49/4:

(39 x)/4 - 27/2 = -49/4

Add 27/2 to both sides:

{y = 1/2 (5 x + 27)

(39 x)/4 = 5/4

Multiply both sides by 4/39:

{y = 1/2 (5 x + 27)

x = 5/39

Substitute x = 5/39 into the first equation:

{y = 539/39

x = 5/39

Collect results in alphabetical order:

Answer: {x = 5/39 , y = 539/39

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Which sequence are geometric? Check all that apply
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Answer:

<h2>10, 7.5, 5.625, 4.21875, ...</h2><h2>160, 40, 10, 2.5, ...</h2><h2>20, 70, 245, 857.5, ...</h2><h2>5, 5.5, 6.05, 6.655, ...</h2>

Step-by-step explanation:

\text{If}\ a,\ b,\ c,\ d,\ e,\ ...\ \text{is a geometric sequence, then}\ \dfrac{b}{a}=\dfrac{c}{b}=\dfrac{d}{c}=\dfrac{e}{d}=....\\\\\#1\\\\\dfrac{7.5}{10}=0.75\\\dfrac{5.625}{7.5}=0.75\\\dfrac{4.21875}{5.625}=0.75\\\boxed{YES}\\================================\\

\#2\\\\\dfrac{40}{160}=\dfrac{1}{4}\\\dfrac{10}{40}=\dfrac{1}{4}\\\dfrac{2.5}{10}=\dfrac{1}{4}\\\boxed{YES}\\================================\\

\#3\\\\\dfrac{70}{20}=3.5\\\dfrac{245}{70}=3.5\\\dfrac{857.5}{245}=3.5\\\boxed{YES}\\================================\\

\#4\\\\\dfrac{16.5}{13}=\dfrac{165}{130}=\dfrac{33}{26}\\\dfrac{20}{16.5}=\dfrac{200}{165}=\dfrac{40}{33}\neq\dfrac{33}{26}\\\boxed{NO}\\================================\\

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\#6\\\\\dfrac{17.1}{16}=1.06875\\\dfrac{18.2}{17.1}=1.0643274..\neq1.06875\\\boxed{NO}

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