4.81- Solving Systems
4.81 a
-2x+3y=1
2x+6y=2
POI (0, 1/3)
4.84 a
Find g(-5)
g(x)=x3-2
-125
4.82
The Math club is baking pies for for a bake sale. The fruit pie recipe calls for twice as many peaches as nectarines. If it takes a total of 168 pieces of fruit for all of the pies, how many nectarines are needed?
Define variables for this problem.
n- nectarines
p- peaches
Candice is solving this system:
2x-1=3y
5(2x-1)+y=32
She notices that the equation contains 2x-1. Can she substitute 3y for 2x-1?
YES!
Which form is equation? How do you know?
y=5x-3
2x+5y=7
y=5x-3
slope intercept, m= slope, b= y-intercept
2x+5y=7
Standard Form- Ax+By=C
4.81 b
y=1/3x+4
x=-3y
POI (-6, 2)
4.84 b
Find g(-5)
g(x)=7+square root(4-x)
10
4.82
The Math club is baking pies for for a bake sale. The fruit pie recipe calls for twice as many peaches as nectarines. If it takes a total of 168 pieces of fruit for all of the pies, how many nectarines are needed?
Write equations for this problem.
2n=p
n+p=168
Candice is solving this system:
2x-1=3y
5(2x-1)+y=32
Substitute 3y for 2x-1 in the second equation. What is that new equation?
5(3y)+y=32
Multiply.
(x-4)(x2-2x-6)
x3-6x2-+2x+24
3x-y=7
y=3x-2
no solution
4.84 c
Find g(-5)
g(x)= cube root (x+(-59))
-4
4.82
The Math club is baking pies for for a bake sale. The fruit pie recipe calls for twice as many peaches as nectarines. If it takes a total of 168 pieces of fruit for all of the pies, how many nectarines are needed?
Which method would be most efficient to solve?
Substitution!
Candice is solving this system:
2x-1=3y
5(2x-1)+y=32
Solve the system for x and y.
Write your answer as an ordered pair labeled POI.
POI (3.5, 2)
Find the equation of the line between the 2 points
(1, 7) and (-2, 9)
y=-2/3+7 2/3
4.81 d
x+2y=1
3x+5y=8
POI (11, -5)
4.84 d
Find g(-5)
g(x)= -4 absolute value (x-1)
-24
4.82
The Math club is baking pies for for a bake sale. The fruit pie recipe calls for twice as many peaches as nectarines. If it takes a total of 168 pieces of fruit for all of the pies, how many nectarines are needed?
Solve the system!
n= 56
p= 112
Candice is solving this system:
2x-1=3y
5(2x-1)+y=32
Show how to check your solution!
Prove it!
Must substitute into BOTH equations to prove answer is correct!
Solve the equation:
2(x-3)+4x+6=9x-10+7x
Not in the book!
4x-6y=2
2x+3y=-5
POI (-1, -1)
Not in book
Find g(-5)
x3+2x-17
-153
4.82
The Math club is baking pies for for a bake sale. The fruit pie recipe calls for twice as many peaches as nectarines. If it takes a total of 168 pieces of fruit for all of the pies, how many nectarines are needed?
Would you write your answer as an ordered pair?
Why or why not?
Write your answer in an acceptable form for this problem.
Sentence makes more sense since no x and y!
56 nectarines are needed.
Not in book and not 4.83
What are the unique solutions for systems of equations?
What do these mean?
infinite solutions- lines coincide
no solution- lines are parallel
Create a short word problem the following equation:
h=5p+7
Define h and p.
Answers vary
5- rate of change
7- starting point