Solving Systems of Linear Equations: Vocabulary
Substitution Method
Graphing Method
Convert to Slope Int. Form
Short Answer
100
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 substitution: y=1 y=x Remember write your answer as an ordered pair.
What is x=1, y=1 or (1, 1)
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 following system of equations by substitution: y=2 3x-5y=5 Remember write your answer as an ordered pair.
What is x=5, y=2 or (5, 2)
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 the system of equations by substitution: y= -4 2x-y=-6 Remember write your answer as an ordered pair.
What is x=-5, y=-4 or (-5, -4)
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? The solution to a system of linear equations is also called this the POI. What does POI stand for?
Answer: The Point of Intersection
400
Solve the following system of equations using the substitution method: y=3x-5 y=7x-13
x = 2 and y = 1 or (2,1)
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
Identify step 2 when solving a system of linear equations with substitution: Step 2: Rewrite the second equation with __________
Answer: Parenthesis
500
Lines that have the same slope and y-intercepts have how many solutions?
Answer: Infinite Solutions
500
Use the substitution method to solve this system of linear equations: y=-7x-3 y=8x+12 Remember write your answer as an ordered pair.
Answer: (-1,4)
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.
Answer: solution
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