Linear Inequalities & Systems of Equations Review
equivalent
Different ways to write the same equation
Zero Slope
a horizontal line
best line of fit
a line on a graph showing the general direction of points
Negative Slope
falls from left to right
x axis
horizontal line on a graph
Rise
moving from down to up/ change in y
Run
moving side to side/ change in x
Solve by elimination
multiply first by something to get rid of one variable then add equations together and sub answer into first equation
Solve by substitution
put one equation into another to solve for the ordered pair
Positive slope
rises from left to right
x-intercept
the point at which the line crosses the x-axis
y-intercept
the point at which the line crosses the y-axis (b)
Undefined Slope
the slope of a vertical line
Solve by graphing
use graph to solve problem
y axis
vertical line on a graph
One solution
when the system of equations have different slopes
origin
(0,0)
graph
A grid of positive and negative areas with an x and y axis
Solution
A value that when substituted makes the statement true.
What does the shading represent?
All of the possible solutions.
less than
Inequality for graph
y < -2x + 3
Inequality for graph
y < 2x + 3
Inequality for graph
y < ½x + 3
Inequality for graph
y > -2x + 3
Inequality for graph
y > -½x + 3
Inequality for graph
y > 2x + 3
Inequality for graph
y > ½x + 3
Inequality for graph
y ≤ -½x + 3
Inequality for graph
y ≤ 2x + 3
Inequality for graph
y ≤ ½x + 3
Inequality for graph
y ≥ -½x + 3
Inequality for graph
y ≥ 2x + 3
Inequality for graph
y ≥ ½x + 3
Inequality for graph
y = mx+b
Slope-intercept form of a line; y = 3x - 5
greater than
Symbol
greater than or equal to
Symbol
less than or equal to
Symbol
Infinitely many solutions
The result when the graphs of the equations are overlapping (coinciding lines)
No solution
The result when the graphs of the equations are parallel lines
Slope
The steepness of a line
Substitution
To replace a variable with a value or expression to simplify an expression or solve an equation
