SOLUTION: If you were to use the substitution method to solve the following system, choose the new system of equations that would result if x was isolated in the second equation.
3x + y +
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Question 633345: If you were to use the substitution method to solve the following system, choose the new system of equations that would result if x was isolated in the second equation.
3x + y + 2z = 1
x + 2y – z = –8
3x – y – 3z = 18
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
3x + y + 2z = 1...............(1)
x + 2y – z = –8...............(2)
3x – y – 3z = 18..............(3)
Take (2)
x + 2y – z = –8
x=z-2y-8......................(4)
Substitute the value of x in (1)
3x + y + 2z = 1...............(1)
3(z-2y-8) + y + 2z = 1
3z-6y-24+y+2z=1
-5y+5z-24=1
-5y+5z=1+24
-5y+5z=25
5(-y+z)=25
5(-y+z)/5=25/5
-y+z=5........................(5)
Substitute the value of x in (3)
3x – y – 3z = 18..............(3)
3(z-2y-8)-y-3z=18
3z-6y-24-y-3z=18
3z-3z-6y-y=18+24
-7y=42
-7y/-7=42/-7
y=-6
Put the value of y in (5)
-y+z=5........................(5)
-(-6)+z=5
6+z=5
z=5-6
z=-1
Put the value of y and z in (4)
x=z-2y-8......................(4)
x=-1-2(-6)-8
x=-1+12-8
x=12-9
x=3
x,y,z=3,-6,-1
Check
=====
Put the value of x,y,z in (1)
3x + y + 2z = 1...............(1)
3(3)+(-6)+2(-1)=1
9-6-2=1
9-8=1
1=1
Put the value of x,y,z in (2)
x + 2y – z = –8...............(2)
3+2(-6)-(-1)=-8
3-12+1=-8
4-12=-8
-8=-8
Put the value of x,y,z in (3)
3x – y – 3z = 18..............(3)
3(3)-(-6)-3(-1)=18
9+6+3=18
18=18
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