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Could you please help me with this very difficult question

Could you please help me with this very difficult question-example-1
User AshvinGudaliya
by
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1 Answer

10 votes
10 votes

Given the system of equations:

x + y + z = -4

2x + 3y - z = -19

-4x - y + 2z = 13

Let's use the elimination method to eliminate the z variable and create a system containing only the x and y variables.

Let's select 2 equations and multiply each equation by values which makes the coefficient of z opposite

Take the first two equations:

x + y + z = -4

2x + 3y - z = -19

Since the coefficients of z are opposite, let's add both equations:

x + y + z = -4

+ 2x + 3y - z = -19

_________________

3x + 4y = -23

Now, take the first and third equations:

x + y + z = -4

-4x - y + 2z = 13

Multiply equation first equation by -2 and add the equations:

-2(x + y + z) = -2(-4)

-4x - y + 2z = 13

-2x - 2y - 2z = 8

+ -4x - y + 2z = 13

_____________________

-6x - 3y = 21

Take the last two equations:

2x + 3y - z = -19

-4x - y + 2z = 13

Multiply the second equation by 2

2(2x + 3y - z) = 2(-19)

-4x - y + 2z = 13

4x + 6y - 2z = -38

-4x - y + 2z = 13

____________________

5y = -25

y = 5

Therefore, we have the equations:

3x + 4y = -23

-6x - 3y = 21

Therefore, the graph of the system is:

ANSWER:

3x + 4y = -23

-6x - 3y = 21

Could you please help me with this very difficult question-example-1
User Matt Blackmon
by
3.0k points