The value x=−8.5
y=15.5
z = 1/2 .
Let's solve the system of equations:
x+y−3z=8
2x−3y+z=−6
3x+4y−2z=20
We can solve the system of equations using elimination.
Steps to solve:
1. Eliminate y:
Multiply the top equation by 3 and the bottom equation by 5:
3x+3y−9z=24
10x−15y+5z=−30
Add the top and bottom equations:
13x−12z=−6
Divide both sides by -12:
x+z=1/2
2. Substitute z back into the top equation:
x+y−3(1/2)=8
x+y−3/2=8
x+y=19/2
3. Solve for y:
y=19/2−x
4. Substitute y back into the equation x+z=1/2:
x+(19/2−x)=1/2
2x+19=2
2x=−17
x=−8.5
5. Substitute x back into the equation y=19/2-x:
y=19/2−(−8.5)
y=19/2+8.5
y=15.5
Question
Solve the following system of equations algebraically using linear combinations and substitutions .
x+y−3z=8
2x−3y+z=−6
3x+4y−2z=20