Download Systems of linear equations 8

Algebra I
Systems of Linear Equations
2016
Mr. Masterjoseph
Name: _________________________
Class: ________
A system of equations can be solved by graphing the equations on the same Cartesian
plane. A solution of a system is an ordered pair that satisfies both equations in the
system. A system of two linear equations can have the following:
A. Exactly one solution – The graphs of the equations intersect at one point. The
system is said to be consistent and independent.
B. No Solution – The graphs of the equation are parallel. There are no ordered pairs
that satisfy both equations. This system is said to be inconsistent.
C. Infinite Number of Solutions – The graphs of the equations are the same line.
An infinite number of points will satisfy both equations. This system is said to be
consistent and dependent.
Use linear combinations to solve the system of linear equations. (Using addition method)
1. 2x + y = 4
x–y=2
2. x - y = 8
x + y = 20
3. x + 3y = 2
-x + 2y = 3
4. x + 4y = 23
-x + y = 2
5. 3x – 2y = 1
2x + 2y = 4
Use linear combinations to solve the system of linear equations. (Using multiplication
method first then addition method)
6. x – y = -5
x + 2y = 4
7. x + 3y = 3
x + 6y = 3
8. 2a + 6y = 4
3a – 7y = 6
Use linear combinations to solve the system of linear equations. (Arranging like terms
method)
9. x + 3y = 12
-3y + x = 30
10. 2x = 7 – 5y
4x – 16 = y