Systems of Linear Equations 58
origin
(0,0)
variable
A letter or symbol that represents a number.
equation
A mathematical sentence that contains an equal sign.
expression
A mathematical sentence without an equal sign.
substitution method
A method of solving a system of equations by replacing one variable with an equivalent expression containing the other variable.
coefficient
A number multiplied by a variable in an algebraic expression or equation.
slope
A ratio comparing the change in output over the change in input of a line. The steepness of a line.
system of equations
A set of two or more equations using the same variables.
intersection point
A solution in ordered pair form that satisfies both functions at the same time.
inconsistent system
A system of equations that has no solution.
constant
A term without a variable
constant
A value that does not change.
point-slope form
A way to write linear equations when you don't know the y-intercept.
linear equation
An equation in two variables whose graph in a coordinate plane is a straight line.
solution of a system of linear equations
Any ordered pair in a system that makes all the equations true. The intersection point.
equivalent
Different ways to write the same equation
standard form
Form for a linear equation: Ax + By = C
point-slope form
Form for a linear equation: y - y1 = m(x - x1 )
slope-intercept form
Form for a linear equation: y = mx + b
Infinite solutions (to a system)
If you have two equivalent lines (the same line), they will have infinite points of intersection. This means that ANY input would yield the same output for both equations.
No solutions (to a system)
If you have two parallel lines, they will never intersect. This means that there is NO input that would yield the same output for both equations.
parallel lines
In a plane, two lines that never intersect. Parallel lines have the same slope.
undefined
No solution. Division by zero = undefined. The slope of a vertical line is undefined.
dependent variable
The outcome; the variable that depends on the input we selected.
1 solution (to a system)
The point (input, output) where the equations intersect. This is the input that would yield the same output in both equations.
undefined
The slope of a vertical line is _________________. (Ex. x = 3)
x-intercept
The value of the input when the output is zero (x, 0). The point where a graph crosses the x-axis. Also called roots, zeros or solutions.
y-intercept
The value of the output when the input is zero (0, y). The point where a graph crosses the y-axis.
independent variable
The variable we can change.
perpendicular lines
Two lines that intersect to form a 90 degree angle. The slopes of perpendicular lines are negative reciprocals.
Arithmetic recursive equation
Use previous (before) term to find the next one
arithmetic sequence
a list of number where every time you add the same number
sequence
a list of numbers
coeficient
a number that is multiplied by a variable
independent system
a system of equations that has exactly one solution
dependent system
a system of equations that has infinitely many solutions
standard form
a,b and c are integers and a is positive number
elimination method
eliminate one of the variables in a system of equations by adding or subtracting the equations
zero slope
ex: x = 8
negative slope
ex: y = -2x
undefined slope
ex: y = 2
positive slope
ex: y = 2x
function
f(x)=ax+b
reciprocal/multiplicative inverse
flip the fraction upside down
x axis
horizontal line on a graph
parallel lines
lines in the same plane that never intersect
Rise
moving from down to up
Run
moving side to side
inverse operations
operations that undo each other
slope/ constant rate of change
rise/run
slope-intercept form
the general way to write a linear equation
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)
zero slope
the slope of a horizontal line (ex. y = 5 )
y axis
vertical line on a graph
