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3 years ago

solve this system of linear equations. separate the x- and y-values with a comma. -12x = -75 - 11y -5x = -89 - 11y

Mathematics

1 answer:

iragen [17]3 years ago

8 0

Answer:

x = -2 , y= -9

Step-by-step explanation:

Solve the following system:

{-12 x = -11 y - 75 | (equation 1)

{-5 x = -11 y - 89 | (equation 2)

Express the system in standard form:

{-(12 x) + 11 y = -75 | (equation 1)

{-(5 x) + 11 y = -89 | (equation 2)

Subtract 5/12 × (equation 1) from equation 2:

{-(12 x) + 11 y = -75 | (equation 1)

{0 x+(77 y)/12 = (-231)/4 | (equation 2)

Multiply equation 2 by 12/77:

{-(12 x) + 11 y = -75 | (equation 1)

{0 x+y = -9 | (equation 2)

Subtract 11 × (equation 2) from equation 1:

{-(12 x)+0 y = 24 | (equation 1)

{0 x+y = -9 | (equation 2)

Divide equation 1 by -12:

{x+0 y = -2 | (equation 1)

{0 x+y = -9 | (equation 2)

Collect results:

Answer: {x = -2 , y= -9

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A.)List the 4 steps outlined in the lesson on solving equations.

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1.) Solve for x:
5 x + 7 = 3 x + 21

Subtract 3 x from both sides:
(5 x - 3 x) + 7 = (3 x - 3 x) + 21

5 x - 3 x = 2 x:
2 x + 7 = (3 x - 3 x) + 21

3 x - 3 x = 0:
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____________________________________________________________
2.) Solve for x:
3 x - 2 (5 - x) = 3 x - 3 (x - 10)

-2 (5 - x) = 2 x - 10:
2 x - 10 + 3 x = 3 x - 3 (x - 10)

Grouping like terms, 3 x + 2 x - 10 = (3 x + 2 x) - 10:
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5 x - 10 = 3 x - 3 (x - 10)

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5 x - 10 = 30 - 3 x + 3 x

3 x - 3 x = 0:
5 x - 10 = 30

Add 10 to both sides:
5 x + (10 - 10) = 10 + 30

10 - 10 = 0:
5 x = 30 + 10

30 + 10 = 40:
5 x = 40

Divide both sides of 5 x = 40 by 5:
(5 x)/5 = 40/5

5/5 = 1:
x = 40/5

The gcd of 40 and 5 is 5, so 40/5 = (5×8)/(5×1) = 5/5×8 = 8:

<span>Answer: x = 8

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3.) Solve for x:</span>
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3 (2 x + 3) = 6 x + 9:
5 (x + 1) = 6 x + 9 + 5

Grouping like terms, 6 x + 5 + 9 = 6 x + (9 + 5):
5 (x + 1) = 6 x + (9 + 5)

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5 (x + 1) = 6 x + 14

Expand out terms of the left hand side:
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Subtract 6 x from both sides:
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5 - 5 = 0:
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14 - 5 = 9:
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Multiply both sides of -x = 9 by -1:
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<span>Answer: x = -9</span>

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