Systems of Linear Equations
the method used where you solve one equation for a variable and plug it into another?
the side of the line that is shaded for the inequality y>-x + 3
above the line
Solve |x - 3|= 7
x = 10 and x= -4
The slope intercept form of a linear equation
y=mx+b
A smoothie shop sells strawberry smoothies for $4 each and banana smoothies for $5 each. One day, they sold a total of 50 smoothies and made $225.How many of each flavor did they sell?
25 of each
Solve the System: y= 2x+3 y= -x + 9
(2,7)
The inequality represented by a dashed line with a slope of 2, y-intercept of -1 , and shading below the dashed line
y<2x-1
The vertex of the function f(x)= |x+4|-2
(-4,-2)
The slope of the line that passes through points (2,3) and (4,7)
m=2
The temperature in a greenhouse fluctuates around a set point of 72 degrees F. On a particular day, the deviation from 72 degrees is modeled by the function T(x)=|x-3|, where t is the hour after 9 am. At what time will the temperature be 2 degrees F above or below 72 degrees F?
10 am and 2pm
This method involves adding or subtracting two equations to eliminate a variable
Elimination
Does the point (4, -2) satisfy the inequality y>1/2x - 3
yes
The vertex of the function y= -2|x-1|+3 and the direction it opens
(1,3) and downward
The equation of the line that passes through (1, -2) and (3,4)
y=3x+5
A freelance designer charges a one-time setup fee plus an hourly rate. After 3 hours, their invoice was $260, and after 7 hours it was $420. Find the function for the invoice and determine the setup fee and hourly rate.
y=40x+140
Solve the System : 2x+3y=12 4x - y =2
(2,2)
The inequality for a graph of a solid line with a slope of 3, y-intercept of 5, and shaded underneath the line
y<= 3x +5
The solution for x of the function f(x)= |3x-5|=7
x=4 and x=-2/3
The equation of a line that passes through (-2,5) and is perpendicular to y=1/3x+4
y=-3x-1
A taxi driver's earnings in dollars depends on the number of hours driven. If she earns $80 in 2 hours and $140 in 5 hours, write the point slope form of her earnings and then convert it to standard form.
y-80=20(x-2)
20x-y=-40
You are told a system has no solution. Graphically, this means the lines are what?
The range of the inequality y>-1/2+5
y>5
The solutions to the inequality y=|2x+1|<5
x>-3 and x<2
Convert the standard form equation to slope-intercept form 3x-2y=8
y=3/2x-4
The graph of the function y>-200
graph