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lora16 [44]
3 years ago
5

4 - 4y = -2 - 9x - 4y = -3

Mathematics
1 answer:
arsen [322]3 years ago
7 0

Answer:

x = -1/3 , y = 3/2

Step-by-step explanation:

Solve the following system:

{4 - 4 y = -2

-9 x - 4 y = -3

Express the system in standard form:

{0 - 4 y = -6

-9 x - 4 y = -3

Express the system in matrix form:

(0 | -4

-9 | -4)(x

y) = (-6

-3)

Write the system in augmented matrix form and use Gaussian elimination:

(0 | -4 | -6

-9 | -4 | -3)

Swap row 1 with row 2:

(-9 | -4 | -3

0 | -4 | -6)

Multiply row 1 by -1:

(9 | 4 | 3

0 | -4 | -6)

Divide row 2 by -2:

(9 | 4 | 3

0 | 2 | 3)

Divide row 2 by 2:

(9 | 4 | 3

0 | 1 | 3/2)

Subtract 4 × (row 2) from row 1:

(9 | 0 | -3

0 | 1 | 3/2)

Divide row 1 by 9:

(1 | 0 | -1/3

0 | 1 | 3/2)

Collect results:

Answer:  {x = -1/3 , y = 3/2

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Determine if (-2,6) and (4,12) are solutions to the system of equations:
kykrilka [37]

Answer:

Both (-2,6) and (4,12) are solutions to the system.

Step-by-step explanation:

In order to determine whether the two given points represent solutions to our system of equations, we must "plug" thos points into both equations and check that the equality remains valid.

Step 1: Plug (-2,6) into y=x+8

(6) = (-2)+8 = 6

The solution verifies the equation.

Step 2: Plug (-2,6) into 2y=x^2 + 8

2(6) = (-2)^2+8=4+8=12

The solution verifies both equations. Therefore, (-2,6) is a solution to this system.

Now we must check if the second point is also valid.

Step 3: Plug (4,12) into y=x+8

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Step 4: Plug (4,12) into 2y=x^2 + 8

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The solution verifies both equations. Therefore, (4,12) is another solution to this system.

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