Graphing
What is the main thing we look for when deciding to solve by graphing?
Equations in slope intercept form
What is the main thing we look for when deciding to use the substitution method? (hint: it's two words)
Isolated Variable
What is the main thing we look for when deciding to use the elimination method?
Same leading coefficients with the same variable terms
Where do I look to find my solutions for systems of inequalities?
If a system of equations has infinite solutions, how do we name it?
Consistent and dependent
Solve the following system of equations:
y = -6x
y = -4x + 2
Solution: (-1,6)
A variable needs to be eliminated to solve the system of equations below. What is the correct first step? Include the operation and which variable we are eliminating.
8x + 6y = 66
8x - 4y = -4
Subtract to eliminate x
What are the two inequality signs that I look for to know that I need to have a dashed boundary line?
< or >
Rewrite the following equations in slope-intercept form:
4y + 8x = -12
-7y = -21x - 7
y = -2x - 3
y = 3x + 1
Solve the following system of equations:
y = 2x
-3x + 8y = 26
Solution: (2,4)
Solve the following system of equations:
6x + 2y = 16
2x - 2y = 32
Solution: (6, -10)
If I multiply or divide an inequality by a negative number, what happens to my inequality symbol?
It flips
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
−3x + y =−5
−6x + 2y = −10
Infinitely many solutions
Solve the following system of equations:
3y + 4 = x
4x - 5y = 23
Solution: (7,1)
Solve the following system of equations:
2x + 3y = 4
4x - 6y = 32
Solution: (5,-2)
For the following linear inequality, do I shade above or below my boundary line?
-3y - 6x > 12
BELOW
Draw and label the TYPES OF LINES we would expect to see for:
A) One solution
B) No solution
C) Infinite solutions
A) Intersecting lines
B) Parallel lines
C) The same line (OR overlapping lines)
Solve the following system of equations:
-2x + y = 10
3x + 10y = 31
Solution: (-3,4)
Solve the following system of equations:
7x - 8y = 22
-2x + 3y = -12
Prove whether or not the point (2,5) is a solution for the following system of inequalities.
y < 6x - 2
y > -x - 8
It is a solution.
5 < 6(2) - 2
5 < 10
AND
5 > -2-8
5 > -10