Systems of Equations: A Short Review dm

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

This system has _____ solutions

• 0
• 1
• 2
• Infinitely many

Solve by graphing.

y = 2x + 1

y = 4x - 1

• (1,3)
• (-1,-3)
• (-1,3)
• (3,1)

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

• Intersecting lines
• Identical (same) line

• Parallel lines

Solve by substitution.

y = -6x + 5

-2x + y = 5

• (-3, -6)
• (-6, 3)
• (0, 5)
• (-3, 5)

Solve by substitution.

y = -3x + 11

y = -6x - 13

• (-8, 35)
• (8, -13)
• (1, 8)
• (2, 13)

Solve using substitution. You will need to rewrite an equation first, solving for a variable:

3x + 2y = 16

7x + y = 19

• (-2,5)
• (-2,-5)
• (2,-5)
• (2,5)

Solve the system by substitution.   5x + 4y = −14 and y =  −7x  −  15 

• (-2, -1)
• (1, -2)
• (-2, 1)
• (-1, -2)

Solve the System using Elimination.
7x - y = -10
-7x + 5y = -6

• (-2, -4)
• (-2, -1)
• (-4, -1)
• (6, -8)

Solve the System using Elimination.

-12x - 4y = -8   

-6x - 2y = -4

• no solution 
• (0,0)
• infinite solutions 
• (4,0)