What is the first step in solving a system with linear equations?
Fill in the blank.
Identify the isolated ________.
Answer: Variable
100
Solve the following system of equations by graphing. Identify the number of solutions; One, (write answer as an ordered pair) None, or Infinite and why?
y=3x-4
y=3x-4
Answer: No Solution because the slopes are the same. Therefore, the lines are parallel.
100
Identify the slope in the this linear equation:
y=2/3x-5
Answer: Slope =2/3
100
If both equations in a system have the different slopes and y intercepts, how many solution exist to the equations?
Answer: One solution
200
What are the two methods to solving systems of linear equations that we have discussed so far?
Answer: Graphing and Substitution
200
Solve the system of equations by graphing.
y=-3/4x+2
y=1/4x-2
Remember write your answer as an ordered pair.
Answer: The solution is (4,-1)
200
Identify the y-intercept in the following linear equation:
y=-2x-6
Answer: y=-6 or (0,-6)
200
This word is used to describe "replacing" a number into an equation for a variable.
Answer: Substitute
300
The solution to a system of linear equations is always written as an ________ ________.
Answer: Ordered pair
300
Solve each system of linear equations by graphing. Identify the number of solutions: One (write as an ordered pair), None, or Infinite.
y=-1/2x+3
y=-1/2x+3
Answer: Infinite solutions because the slopes and y intercepts are the same. (The equations are the same.)
300
Convert to slope intercept form:
4x+2y=2
Answer: y=-2x+1
300
If the slopes are the same but the y-intercepts are different, how many solutions are there? Why?
Answer: No solution because they don't intersect (they are parallel)
400
Daily Double: What's your wager? Parallel lines form this type of solution.
Answer: No Solution
400
Solve the system of linear equations using the graphing method.
y=-1/3x-2
y=2/3x+1
Answer: (-3,-1)
400
Convert to standard form:
3x+9y=-18
y=-3x-2
400
What is another word for substitution (think sports!)?
Answer: Parenthesis
500
Lines that have the same slope and y-intercepts have how many solutions?
Answer: Infinite Solutions
500
Daily Double: What's your wager?
Wager:______
Graph x=-3 and describe the slope. Is it undefined or zero?
Answer: The slope is undefined and vertical at (-3,0).
500
Convert to slope intercept form:
5x+4y=-12
Answer: -4/5x-3
500
Fill in the blank.
The point of intersection is the same as the __________ to a system of equations.