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# chapter 3

### solving equations and system of equations

Break-even point when cosy of production equals the income from selling a product
column numbers aligned vertically in a matrix
consistent a system that has at least one solution
dependent a system that has infinitely many solutions, when graphed it is the same line
dimensions of matrix it is the number of rows by the number of columns of a matrix, written m x n
element each of the number in a matrix
inconsistent a system that has no solution. if graphed the lines are parallel
intersection of graphs for solving an equations graph y1= left of the equation. y2= right side of the equation. the x-component of the intersection is the solution
interval notation solution written in the form of (2,∞) or (-∞,6] as examples
linear inequality similar to a linear equation except the equality symbol is replaced with<,>, ect.
matrix a rectangular array of numbers
matrix addition when two or more matrices with the same dimensions are added by adding the elements in the same position together
row numbers aligned horizontally in a matrix
scalar multiplication when a number in front of the matrix is multiplied by every element inside the matrix to get a product with the same dimensions as the original matrix
set notation solution written in the form of {x|x<2} as an example
solution of a system in two variables it is in the form of (x,y), in three variables it looked like (x,y,z). various variables may be used to represent the ordered pair or ordered triple. when graphed it is the intersection of the lines at one point.
solution to a system of inequalities represented by a graph and shading of all points that satisfy all linear inequalities. commonly shaded area on the graph.
substitution method the process is to take on equation and solve for one variable. the expression for that variable is then replaced for the variable in another equation
system of equations two or more equations in tow or more variables are solved simultaneously
x-intercept method for solving an equation written so that one side of the equation equals 0. graph y1=the nonzero side of the equation. find the x-intercept or zero of the graph. the x-coordinate of the x-intercept is the solution.
Created by: dcharm