Systems of Equations
Parallel Lines (BONUS: No Solution)
Are the equations y=-x+2 and y=-x-4 Parallel Lines, Intersecting Lines, or Coinciding Lines? BONUS: Do the equations have No Solution, One Solution, or Infinite Solutions?
(2,3)
At what point do the equations y=-x+5 and y=x+1 intersect? Do not use substitution (you will need graph paper). For extra practice, verify your answer
No, No, Yes
Does the point (0,4) make the equations y=-2x and y=x+3 true? Does the point (2,5) make the equation true? Does the point (-1,2) make the equations true? (Hint: Substitute the point into the equation).
(7,6)
Find the solution for the equations -3x+y=-15 and -3x+6y=15 using substitution
(3,4)
Find the solution for the equations -5m+9n=21 and 2m+2n=14 using the Addition/Subtraction Method (Hint: Multiply or Divide)
(-1,-7)
Find the solution for the equations -9x+y=-2 and y=x-6 using substitution
(26,68)
Find the solution for the equations 11x-4y=14 and -2x+y=16 using the Addition/Subtraction Method (Hint: Multiply or Divide)
(1,2)
Find the solution for the equations 3x+2y=7 and 5x-2y=1 using the Addition/Subtraction Method
(4/9,-3/5)
Find the solution for the equations 9y+5z=1 and -9y-10z=2 using the Addition/Subtraction Method
(2,1/5)
Find the solution for the equations t=-4/5s-7/5 and 2s-5t=3 using the Addition/Subtraction Method
(-2,-3)
Find the solution for the equations y=6x+9 and y=3x+3 using substitution
(1,-2), y=-3x+1, y=2x-4
In the example, at what point do the two lines intersect? What is the equation for both lines? (Hint: Slope-Intercept Form). Start with the red line when typing your answer. For extra practice, verify your answer
Intersect
The point that two lines _________ is the solution to the system
Both
To solve a system of linear equations, the ordered pair must work for ____ equation(s)
Coinciding Lines (Same Lines)
Will always intersect (because they are the same line). Have all ordered pairs on line in common (where lines intersect)
Parallel Lines
Will never intersect. No ordered pairs in common
Intersecting Lines
Will only intersect once. Have one ordered pair in common (where lines intersect)
Parallel Lines
________ _____ have the same slope and different y-intercepts
Coinciding Lines (Same Lines)
__________ _____ have the same slope and the same y-intercept
Intersecting Lines
____________ _____ have a different slope (the y-intercept doesn't matter)
Solution
An ordered pair that makes a linear equation TRUE is called a ________
Parallel Lines (BONUS: No Solution)
Are the equations 2x-y=8 and -2x+y=8 Parallel Lines, Intersecting Lines, or Coinciding Lines? BONUS: Do the equations have No Solution, One Solution, or Infinite Solution?
Intersecting Lines (BONUS: One Solution)
Are the equations x+y=5 and x-y=-3 Parallel Lines, Intersecting Lines, or Coinciding Lines? BONUS: Do the equations have No Solution, One Solution, or Infinite Solution?
