Solve Linear System
Solve the linear system by substitution:
y=4x+3
5x+2y=19
(1,7)
Write a linear system to model this problem:
Jane made 150 baked goods for a fundraiser. The baked goods were brownies and cookies. The cost per brownie was $0.75 and the cost per cookie was $0.50. Jane raised $91.25.
*Remember to define variables
let b= the number of brownies
let c= the number of cookies
0.75b+0.50c=91.25
b+c=150
What is the name given to lines that occupy the exact same space on a coordinate grid (lines that have equivalent equations)?
coincident
Factor
4k^2-225h^2
(2k-15h)(2k+15h)
What is the formula for the volume of a rectangular prism?
V=lwh
Solve the linear system by elimination:
x+3y=9
-2x+5y=4
(3,2)
Solve the linear system:
Jane made 150 baked goods for a fundraiser. The baked goods were brownies and cookies. The cost per brownie was $0.75 and the cost per cookie was $0.50. Jane raised $91.25. How many brownies and how many cookies did Jane sell?
65 brownies, 85 cookies
Given the equation, 2x+5y=9, write a second equation that would make the system have no solution. ANSWERS MAY VARY. GIVE YOUR ANSWER IN SLOPE-INTERCEPT FORM.
PARALLEL LINE- same slope, different y-intercept
y=-2/5x+11
Write an equation in general form for the line that passes through U(-5, 7) and is perpendicular to the line:
y=3/4x+8
4x+3y-1=0
Simplify
(x^4)(x^(1/5))
x^(21/5)
Solve the linear system by graphing:
x-4y=6
2y=-2x+2
(2,-1)
Model this situation with a linear system:
A rectangular fence has a length,l, that is 7 cm longer than its width, w. Its perimeter is 82 cm.
DO NOT SOLVE THE SYSTEM
l=w+7
2l+2w=82
Given the equation, 4x+5y=11, write a second equation that would make the system have one solution. ANSWERS MAY VARY. GIVE YOUR ANSWER IN SLOPE-INTERCEPT FORM.
y=3x+11
(different slope)
***DAILY DOUBLE***
What is the difference between general form and standard form?
General form has all terms on one side equal to 0, whereas standard form has the terms with variables on one side equal to the constant term (term that does not contain variable)
Factor
4x^2-27x+18
(4x-3)(x-6)
Solve the linear system by elimination:
2a+4b=32
5a+3b=10
(-4, 10)
Solve the linear system:
A rectangular fence has a length,l, that is 7 cm longer than its width, w. Its perimeter is 82 cm.
The width of the fence is 17 metres and the length of the fence is 24 metres.
State the number of solutions to the linear system below.
3x+5y=10
4x+5y=20
one
Write this equation in standard form:
y-9=1/5(x+3)
x-5y=-48
What is the difference between the formulas for the volume of a rectangular pyramid and the volume of a rectangular prism?
A rectangular pyramid is one-third the volume of a rectangular prism.
OR
A rectangular prism is 3 times the volume of a rectangular pyramid.
***DAILY DOUBLE***
Solve the linear system:
3/10x+1/2y=4/5
1/7x+1/3y=-2/21
(11, -5)
Jill has a cup of nickels and a cup of dimes. The total number of coins is 253 and their value is $19.05. How many coins are in each cup?
125 nickels, 128 dimes
Given the equation,
3/4x+5/2y=8
write a second equation that would make the system have infinite solutions. ANSWERS MAY VARY. GIVE YOUR ANSWER IN STANDARD FORM.
3x+10y=32
***DAILY DOUBLE***
Simplify- do not leave any negative exponents in your answer.
((5x^-2y^(1/2))/(15x^2y^(3/2)))^3
1/(27x^12y^3
Use exponent laws to simplify:
(root3x)(root5(x^3))
x^(14/15)