Worksheets3 Variable Linear Systems of Equations
Total questions: 11
Worksheet time: 55mins
Solve the system of equations:
x+5y−3z=22
3x−4y+2z=−13
2x+3y+4z=3
x=1, y=3, z=−2
x=−1, y=−3, z=2
x=1, y=−3, z=2
x=1, y=3, z=2
If you run into a mathematical statement such as 0=0 when solving a system of 3 linear equations, then the system has (a) solutions.
If you run into a mathematical statement such as 0=4 when solving a system of 3 linear equations, then the system has (a) solutions.
Solve the system of equations:
2x−3y=3z−7
4z−2x+3y=12
4y+2z−3x=0
Note: don't forget to make sure the equations are written in standard form.
x=2, y=4, z=5
x=−2, y=−4, z=5
x=−2, y=4, z=−4
x=−2, y=−4, z=−5
Solve the system of equations:
2x+3y−5z=61
x+2y+4z=−5
3x+2y−3z=47
x=5, y=7, z=−6
x=−5, y=7, z=−6
x=5, y=−7, z=6
x=5, y=7, z=6
Solve the system of equations:
2x+6y+4z=8
−4x+7y+5z=27
6x+5y−8z=39
x=3, y=−5, z=−4
x=−3, y=−5, z=4
x=3, y=5, z=4
x=−3, y=5, z=−4
Solve the system of equations:
4x+3y+3z=2
3x+7y=2z−78
5z+4x+4y=20
x=−4, y=6, z=12
x=−4, y=−6, z=12
x=4, y=−6, z=12
x=4, y=6, z=12
Solve the system of equations:
x+y+z=2
2x+2y+2z=4
−3x−3y−3z=−6
x=0, y=0, z=0
x=1, y=1, z=2
No solution
Infinite solutions
Solve the system of equations:
x−y−2z=4
4x−4y−z=2
−x+y+2z=−3
x=1, y=−1, z=0
x=0, y=0, z=1
No solution
Infinite solutions
Solve the system of equations:
f+g+h=13
f−h=−2
−2f+g=3
x=2, y=−7, z=−4
x=2, y=7, z=4
No solution
Infinite solutions
Andrea sells photographs at art fairs. She prices the photos according to size: small photos cost $10, medium photos cost $15, and large photos cost $40. She usually sells as many small photos as medium and large photos combined. She also sells twice as many medium photos as large. A booth at the art fair costs $300.
If her sales go as usual, she will have to sell (a) small photos to pay for the booth.
