For the given linear system equations, the value for the variables are: x=-2, y=4, and z=-5 - Option C.
System of Linear Equations
System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
The question gives:
2x+y-5z=4 (1)
x+3y+z=5 (2)
3x-y-4z=-11 (3)
First, you should sum equations 1 and 2. The results will be:
3x+4y-4z=9 then you have a new equation (4).
3x-y-4z=-11 (3)
3x+4y-4z= 9(4)
Now, you should multiply equation (3) by -1, then you will have:
-3x+y+4z=+11 (3)
3x+4y-4z=9 (4)
After that, you should sum the previous equations: (3) and (4).
5y=20
y=4
For find z, you should multiply equation 2 by -2. After that, you should sum equations 1 and 2.
2x+y-5z=4 (1)
-2x-6y-2z=-10 (2)
Thus, you will have:
-5y-7z=-6, like y=4 you have
-5*4-7z=-6
-20-7z=-6
-7z=14
z=-2
If z=-2 and y=4 from equation 2, you can find x.
x+3y+z=5
x+3*4-2=5
x+12-2=5
x+10=5
x=5-10
x=-5
Read more about the solving systems equations here:
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