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An equation is a statement that two quantities are equal, or the same, identical, in value. It is expressed by putting an equal sign (=) between the two quantities. An inequality is a statement that two quantities are not equal, or more specifically, that one is less than the other, or less than or equal to the other. It is expressed with the unequal sign (an equal sign with a slash through it), a less than sign (<), a greater than sign (>), or a less than or equal sign or greater than or equal sign. A less than or equal sign looks like a less than sign with an underscore; similarly for the greater than or equal sign.
Answer 1
A linear equation may be represented by all the points on a straight line.
A linear inequality would be represented by all points in the plane on one side or the other of the line which is determined by the corresponding equation. The line itself may or may not be part of the solution.
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How many solution sets do systems of linear inequalities have Must solutions to systems of linear inequalities satisfy both inequalities In what case might they not?
A solution to a linear inequality in two variables is an ordered pair (x, y) that makes the inequality a true statement. The solution set is the set of all solutions to the inequality. The solution set to an inequality in two variables is typically a region in the xy-plane, which means that there are infinitely many solutions. Sometimes a solution set must satisfy two inequalities in a system of linear inequalities in two variables. If it does not satisfy both inequalities then it is not a solution.
What makes a system of equations dependent?
If one (or more) of the equations can be expressed as a linear combination of the others. This is equivalent to the statements the matrix of coefficients does not have an inverse (or is singular), or the determinant of the matrix of coefficients is zero.
What makes two linear equations either parallel or perpendicular to each other?
Depending on the value of the slope or gradient if its the same then they are parallel if its a reciprocal then they are perpendicular.
What is the purpose of Cramer's rule?
In math, the purpose of Cramer's rule is to be able to find the solution of a system of linear equations by using determinants and matrices. Cramer's rule makes it easy to find a system of equations that have many unknown variables.
How do to clear decimals when solving linear equations and inequalities?
Multiply both sides of each linear equation by a power of 10 that is sufficiently large to clear the decimal. Example: 0.34x = 13.6. There are two places to the right of the decimal point, on the left side; there is one place to the right of the decimal point, on the right side. If you multiply both sides by 100, you get 34x = 1,360. That result clears all decimals, and you might find it easier to solve. You don't have to do that, but many will say that that makes it easier for them.
