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