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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.
Why should you clear decimals when solving linear equations and inequalities?
It makes it allot less confusing. But, that is just my opinion.
What is the feasible region in linear programming?
Linear programming is just graphing a bunch of linear inequalities. Remember that when you graph inequalities, you need to shade the "good" region - pick a point that is not on the line, put it in the inequality, and the it the point makes the inequality true (like 0
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 is the importance of slope intercept form?
makes it very easy to graph linear equations
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.
How does solving linear inequalities differ from solving linear equations?
Linear inequalities are equations, but instead of an equal sign, it has either a greater than, greater than or equal to, less than, or a less than or equal to sign. Both can be graphed. Solving linear equations mainly differs from solving linear inequalities in the form of the solution. 1. Linear equation. For each linear equation in x, there is only one value of x (solution) that makes the equation true. Example 1. The equation: x - 3 = 7 has one solution, that is x = 10. Example 2. The equation: 3x + 4 = 13 has one solution that is x = 3. 2. Linear inequality. On the contrary, a linear inequality has an infinity of solutions, meaning there is an infinity of values of x that make the inequality true. All these x values constitute the "solution set" of the inequality. The answers of a linear inequality are expressed in the form of intervals. Example 3. The linear inequality x + 5 < 9 has as solution: x < 4. The solution set of this inequality is the interval (-infinity, 4) Example 4. The inequality 4x - 3 > 5 has as solution x > 2. The solution set is the interval (2, +infinity). The intervals can be open, closed, and half closed. Example: The open interval (1, 4) ; the 2 endpoints 1 and 4 are not included in the solution set. Example: The closed interval [-2, 5] ; the 2 end points -2 and 5 are included. Example : The half-closed interval [3, +infinity) ; the end point 3 is included.
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.
Whats Difference between linear equation to linear function?
A linear equation contains only the first power of the unknown quantity. Thus, 5x - 3 = 7 and x/6 = 4 are both linear equations. Linear equations have only one solution which is the value of the unknown that when substituted in the equation , makes the left hand side equal to the right hand side.Linear functions have the same limitation in terms of only containing the first power of the unknown quantity. They yield graphs that are straight lines and thus the name 'linear' is used. A simple linear function is f:x →2x + 1. This can also be written as f(x) = 2x + 1 or another identifying letter used such as y = 2x + 1. Consequently, for different values of the unknown quantity (in this case 'x') then the function also yields a different value.
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.
How does solving linear inequality differ from solving linear equation?
Linear inequalities are equations, but instead of an equal sign, it has either a greater than, greater than or equal to, less than, or a less than or equal to sign. Both can be graphed. Solving linear equations mainly differs from solving linear inequalities in the form of the solution. 1. Linear equation. For each linear equation in x, there is only one value of x (solution) that makes the equation true. The equation: x - 3 = 7 has one solution, that is x = 10. The equation: 3x + 4 = 13 has one solution that is x = 3. 2. Linear inequality. On the contrary, a linear inequality has an infinity of solutions, meaning there is an infinity of value of x that make the inequality true. All these x values constitute the "solution set" of the inequality. The answers of a linear inequality are expressed in the form of intervals. The linear inequality x + 5 < 9 has as solution: x < 4. The solution set of this inequality is the interval (-infinity, 4) The inequality 4x - 3 > 5 has as solution x > 2. The solution set is the interval (2, +infinity). The intervals can be open, closed, and half closed. The open interval (1, 4) ; the 2 endpoints 1 and 4 are not included in the solution set. The closed interval [-2, 5] ; the 2 end points -2 and 5 are included. The half-closed interval [3, +infinity) ; the end point 3 is included.
What is linear equation in one variable?
Linear equations with one variable will either be horizontal or vertical lines. y=2 is a horizontal line going through (0,2)
